Zirconium and Hafnium Boride Alloy Templates on Silicon for Nitride Integration Applications

ABSTRACT

Semiconductor structures are provided comprising a substrate and a epitaxial layer formed over the substrate, wherein the epitaxial layer comprises B; and one or more element selected from the group consisting of Zr, Hf and Al and has a thickness greater than 50 nm. Further, methods for integrating Group III nitrides onto a substrate comprising, forming an epitaxial buffer layer of a diboride of Zr, Hf, Al, or mixtures thereof, over a substrate; and forming a Group III nitride layer over the buffer layer, are provided which serve to thermally decouple the buffer layer from the underlying substrate, thereby greatly reducing the strain induced in the semiconductor structures upon fabrication and/or operation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of the filing dates, under 35 USC§119(e), of U.S. Provisional Application Ser. No. 60/883,477, filed Jan.4, 2007; and U.S. Provisional Application Ser. No. 60/973,002, filedSep. 17, 2007, each of which are hereby incorporated by reference intheir entirety.

STATEMENT OF GOVERNMENT FUNDING

The invention described herein was made in part with government supportunder grant number EEC-0438400, awarded by the National ScienceFoundation. The United States Government has certain rights in theinvention.

FIELD OF THE INVENTION

The invention generally relates to the preparation and use of epitaxialbuffer layers in the preparation of Group III-N materials on solidsupports. In particular, the invention relates to the use of epitaxialdiboride buffer layers on semiconductor substrates for use in thepreparation of Group III-N overlayers.

BACKGROUND OF THE INVENTION

Group III nitride materials include gallium nitride (GaN), aluminumnitride (AlN), indium nitride (InN) and their alloys such as aluminumgallium nitride (AlGaN), indium gallium nitride (InGaN), and aluminumindium gallium nitride (AlInGaN). These materials are semiconductorcompounds that have a wide direct bandgap, which permits highlyenergetic electronic transitions to occur. Such electronic transitionscan result in group III nitride materials having a number of attractiveproperties including the ability to efficiently emit blue andultraviolet light, the ability to transmit signals at high frequency,and others. Accordingly, group III nitride materials are being widelyinvestigated in many semiconductor device applications, includingmicroelectronic devices such as transistors, and optoelectronic devicessuch as laser diodes and light emitting diodes (LEDs).

Group III nitride materials have been formed on a number of differentsubstrates including sapphire, silicon (Si), and silicon carbide (SiC).Semiconductor structures, such as doped regions, may then be formedwithin the group III nitride material region. There are many advantagesof growing group III nitrides, such as GaN, on Si substrates, animportant one of which is the integration with Si-based electronics andthe availability of very large area substrates. Previously, however,semiconductor structures having group III nitrides formed on Sisubstrates have presented significant drawbacks. Such structures havebeen complicated and expensive to fabricate. Moreover, light emittingoptoelectronic devices having group III nitrides formed on siliconsubstrates are less efficient than such devices formed on sapphiresubstrates. In optoelectronic applications, Si is approximately 45%absorbing in the ultraviolet (UV) region, while sapphire is totallytransparent (see, Aspnes, et al. Phys. Rev. B 27, 985 (1983)). Thus, alight-emitting optoelectronic device based on group III nitrides will beless efficient if Si(111) is used as a substrate than if sapphire isused as a substrate.

The growth of group III nitrides, including GaN, is most commonlyaccomplished by heteroepitaxy using methods of metal organic chemicalvapor deposition (MOCVD) and molecular beam epitaxy (MBE). Thesubstrates employed are generally sapphire and α-SiC(0001), which havelattice mismatches of 16% and 3.6% respectively with GaN. Coupled withmismatches in thermal expansion coefficients, the misfit dislocationsproduced in GaN during heteroepitaxial growth pose a limitation to theultimate performance of nitride-based electronics. Various growthschemes involving patterned substrates have been developed to improvethe dislocation density. These growth schemes include, for example,epitaxy by lateral overgrowth (ELOG), which is described in Kato, et al.J. Cryst. Growth 144, 133 (1994), and pendeoepitaxy (PE), which isdescribed in Linthicum et al, Appl. Phys. Lett. 75, 196 (1999).Nevertheless, the quest for lattice-matched substrates continues. BulkGaN crystals grown under high pressures, as described by Porowski, J.Cryst. Growth 189/190, 153 (1998), have been used as substrates. Suchsubstrates, however, are hampered by their small size. Another approachto homoepitaxy is the growth of thick GaN layers by hydride vapor phaseepitaxy (HVPE), which is described by Molnar, et al., J. Cryst. Growth178, 147 (1997). These substrates, however, suffer from poorcrystallinity and the highly strained layers often develop cracks andother undesirable morphologies.

Kinoshita et al. Jpn. J. Appl. Phys., pt. 2, 40, L1280 (2001) havereported the growth of single crystals of zirconium diboride, ZrB₂(0001)to provide an electrically conductive lattice-matched substrate for GaNgrowth. ZrB₂ has a hexagonal structure with lattice constants a=3.169 Åand c=3.530 Å. The in-plane lattice constant has about 0.6% mismatchwith that of GaN (a=3.189 Å). The thermal expansion coefficients along[1010] on the basal plane are also well-matched between ZrB₂ and GaN,being 5.9×10⁻⁶ K⁻¹ and 5.6×10⁻⁶ K⁻¹ respectively. While thesesimilarities in thermal properties between ZrB₂ and GaN suggest that theuse of ZrB₂ (0001) as a substrate for the growth of GaN films may leadto a reduction of both dislocation density and biaxial strain in theGaN, significant drawbacks still limit the use of ZrB₂ as a substratefor the growth of GaN films. One such drawback is the high temperaturerequired to prepare single crystals of ZrB₂. Preparation of thesecrystals requires very high temperatures since the melting point of ZrB₂is 3220° C. A float-zone method has been developed, as described byOtani, et al., J. Cryst. Growth 165, 319 (1996), in which a 1-cmdiameter rod was isostatically pressed at 1700° C. from ZrB₂ powder andmelted in a floating zone by radio frequency (RF) heating. The moltenzone was about 0.5 cm long and a growth rate of 2-3 cm per hour wasobtained, as described by Otani et al. and Kinoshita et al. The ZrB₂single crystals thus grown, however, have size limitations.

A typical size of such a crystal of ZrB₂ is 1 cm in diameter and 6 cmlong. Successful epitaxial and strain-free GaN and AlN growth on suchsingle crystals of ZrB₂ using MBE and MOCVD, respectively, have beenreported, respectively by Suda et al., J. Cryst. Growth 237-239, 1114(2002) and Liu et al., Appl. Phys. Lett. 81, 3182 (2002). However, thesize limitation of the ZrB₂ substrate remains an unresolved issue.

SUMMARY OF THE INVENTION

In a first aspect, the invention provides a semiconductor structurecomprising a substrate and an epitaxial layer formed over the substrate,wherein the epitaxial layer comprises B (boron) and one or more elementselected from the group consisting of Zr, Hf and Al; and the epitaxiallayer has a thickness greater than 50 nm.

In a second aspect, the invention provides methods for forming anepitaxial buffer layer over a substrate comprising, contacting asubstrate with a precursor gas at a temperature and a pressure suitablefor depositing an epitaxial buffer layer over the substrate, theepitaxial buffer layer having a thickness of greater than about 50 nm,wherein the precursor gas comprises (i) about 0.1-5 v/v % Zr(BH₄)₄,Hf(BH₄)₄, an Al source, or mixtures thereof, and (ii) hydrogen.

In a third aspect, the invention provides a method for integrating GroupIII nitrides onto a substrate comprising, forming a buffer layer of adiboride of Zr, Hf, Al, or mixtures thereof, having a thickness greaterthan about 50 nm over a substrate; and forming a Group III nitride layerover the buffer layer.

In a fourth aspect, the invention provides a method for forming anAl_(x)Ga_(1−x)N layer over a substrate comprising, contacting asubstrate with H₂GaN₃, D₂GaN₃, or mixtures thereof in the presence of anAl source at a temperature and a pressure to form a Al_(x)Ga_(1−x)Nlayer, wherein the temperature is less than about 800° C.

In a fifth aspect, the invention provides a method for tuning thereflectivity of a buffer layer comprising, forming a buffer layer of analloy of the formula Hf_(x)Zr_(1−x)B₂ having a thickness greater thanabout 50 nm and a reflectivity over a substrate, wherein x is apredetermined value from 0 to 1, and wherein the reflectivity of thebuffer layer is greater than a layer of ZrB₂ having an similar thicknessas the buffer layer.

In a sixth aspect, the invention provides a method for tuning thelattice constant of a buffer layer comprising, forming a buffer layer ofan alloy of the formula Hf_(x)Zr_(1−x)B₂ having a thickness greater thanabout 50 nm, and forming an active layer over the buffer layer, whereinx is a predetermined value from 0 to 1, and wherein the active layer islattice matched to the buffer layer.

In a seventh aspect, the invention provides a semiconductor structurecomprising, a stack comprising a plurality of repeating alloy layers,formed over a substrate, wherein the repeating alloy layers comprise twoor more alloy layer types, wherein at least one alloy layer typecomprises a Zr_(z)Hf_(y)Al_(1−x−y)B₂, alloy layer, wherein the sum of zand y is less than or equal to 1, and the thickness of the stack isgreater than about 50 nm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an exemplary semiconductor structure of the inventioncomprising a substrate and a layer of the invention, as describedherein, formed over the substrate.

FIG. 2 illustrates an exemplary semiconductor structure of the inventioncomprising a substrate and a layer of the invention, as describedherein, formed over the substrate, and an active layer formed over thelayer of the invention.

FIG. 3 is a typical high resolution XTEM micrograph from a thick ZrB₂film.

FIG. 4 shows the measured a-axis (squares) and c-axis (circles) strainas a function of temperature for the 200 nm thick ZrB₂ film.

FIG. 5 shows them measured a-axis (squares) and c-axis (circles) strainas a function of temperature for the 400 nm thick ZrB₂ film.

FIG. 6 compares the temperature dependence of the measured a- and c-axislattice parameters of the ZrB₂ film (solid squares) to calculatedrelaxed values (open circles) and bulk data from the literature (solidlines).

FIG. 7 is a schematic representation of the strain distribution in thethin and thick ZrB₂/Si heterostructures at the growth temperature of900° C.

FIG. 8 is a comparison of the temperature dependence of the mismatchstrains of GaN with ZrB₂/Si(111) films and bulk ZrB₂ substrates.

FIG. 9( a) shows the electronic band structure of ZrB₂ (the horizontallines denotes the Fermi level).

FIG. 9((b) shows the density of states of ZrB₂ indicating semi-metalliccharacter.

FIG. 9( c) is a “roadmap” of the Brillouin zone used in the bandstructure plot.

FIG. 9( d) illustrates the crystal structure of ZrB₂ (Zr atoms blue, Batoms pink).

FIG. 10 shows the decomposition of the density of states by site (Zr,B)and by angular momentum character; the top-most panel is a plot of theinterstitial contribution.

FIG. 11 is a graph illustrating the real (ε₁) and imaginary (ε₂) partsof the infrared complex dielectric function of ZrB₂ films grown onSi(111).

FIG. 12 is a graph illustrating the real (ε₁) and imaginary (ε₂) partsof the visible-UV complex dielectric function of ZrB₂ films grown onSi(111).

FIG. 13 is a graph showing the reflectivity plot of ZrB₂ films grown onSi(111) (Solid line) derived form ellipsometry IR, Vis and UVmeasurements; the dotted line is a all-electron FPLAPW-DFT simulation;the dot-dashed line is the reflectivity data from bulk ZrB₂ crystals asobtained by Oda and Fukui; the inset is anisotropy in the reflectivitybased on theory (R_(∥) and R_(⊥) are the reflectivities withpolarization parallel and perpendicular to the basal plane,respectively).

FIG. 14 is a graph of the band diagrams for ZrB₂ illustrating theelectronic origin of the spectral features found in the reflectivity at2.2, 4.4 and 5.5 eV; the shaded regions indicate interband transitions,and location in k-space, for which the momentum matrix elementcontributions to the spectral features are largest.

FIG. 15( a) shows RBS spectra of a Zr_(0.70)Hf_(0.30)B₂ film growndirectly on Si(111) in accordance with the invention;

FIG. 15( b) shows an X-ray diffraction (XRD) (113) reciprocal space mapfrom Zr_(0.70)Hf_(0.30)B₂/Si(111);

FIG. 15( c) shows a diffraction contrast micrograph of entire layershowing defect free microstructure and smooth surface. The inset shows ahigh resolution image of the perfectly epitaxial interface;

FIG. 16( a) shows RBS spectra for Hf_(0.5)Zr_(0.5)B₂ alloy layer grownon a ZrB₂ buffer layer;

FIG. 16( b) shows high resolution X-ray reciprocal space maps of the(−113) peaks of Hf_(0.5)Zr_(0.5)B₂ and ZrB₂ buffer layer;

FIG. 17 shows (top) a Z-contrast image of a HfB₂/ZrB₂/Si(111)heterostructure and (bottom) a high resolution XTEM of the perfectlyepitaxial HfB₂/ZrB₂ interface and corresponding EELS composition profileof Hf (M-edge) and Zr (L-edge);

FIG. 18 Real (ε₁) and imaginary (ε₂) parts of the infrared complexdielectric function of HfB₂ films grown on Si(111) via ZrB₂ bufferlayers. The dielectric function is obtained from a point-by-point fit ofthe ellipsometric data, as described in the text.

FIG. 19 Real (ε₁) and imaginary (ε₂) parts of the visible-UV complexdielectric function of a HfB₂ films grown on Si(111) via aHf_(x)Zr_(1−x)B₂ buffer layer. The dielectric function is obtained froma point-by-point fit of the ellipsometric data, as described in thetext;

FIG. 20 Solid line: Optical reflectivity of ZrB₂ films grown on Si(111),calculated from the dielectric function data. Dotted line: Opticalreflectivity of HfB₂ films grown on Si(111) via Hf_(x)Zr_(1−x)B₂ bufferlayers, calculated from the dielectric function data;

FIG. 21 (Left) Optical image of the surface morphology for a ZrB₂ filmgrown on an on-axis Si(111) wafer showing the presence of large islands.The areas in between islands are smooth with a nominal AFM RMS of ˜2.5nm. (Right) Corresponding image of a film grown on a 4 degree miscutSi(111) showing that the surface is essentially featureless. AFM imagesindicate a highly homogeneous surface roughness.

FIG. 22 is a cross-sectional transmission electron microscopy (XTEM)image showing the microstructure of a GaN/ZrB₂/Si(111) semiconductorstructure according to the invention;

FIG. 23 is a PL spectrum of a GaN/ZrB₂/Si(111) semiconductor structureaccording to the invention;

FIG. 24( a) shows a micrograph illustrating a AlGaN/GaN/ZrB₂/Si(111)structure;

FIG. 24( b) shows a typical cathodoluminescence spectrum from the sampleof FIG. 24( a) exhibiting strong band gap emission peaks with awavelength maximum at 346 nm which corresponds to a composition ofAl_(0.10)Ga_(0.90)N;

FIG. 25 is a cross section of a buffer region of a semiconductor devicein accordance with the invention;

DETAILED DESCRIPTION OF THE INVENTION

In a first aspect, the invention provides a semiconductor structurecomprising a substrate and an epitaxial layer comprising B and one ormore elements selected from the group consisting of Zr, Hf, and Al,formed by epitaxy formed over the substrate, wherein the epitaxial layerhas a thickness greater than 50 nm.

The semiconductor structures of the present invention can be used, forexample, to help support the growth of group III nitride materials on asubstrate. In one non-limiting example, the epitaxial layer can serve asa buffer layer for growth of group III nitride materials on a substrate,for example, where the buffer layer is thermally decoupled (notthermally pinned) to the underlying substrate. Such buffer layers havethe advantage of reducing the strain imposed on the semiconductorstructure by the thermal cycling involved in semiconductor process andoperation. Such resulting semiconductor structures having group IIInitride materials can be used for active semiconductor devices, such astransistors, field emitters, light-emitting optoelectronic devices, andoptoelectronic devices.

Referring to FIG. 1, according to a first aspect of the invention, asemiconductor structure is provided comprising a substrate (1800) and anepitaxial layer (1801) formed over the substrate. Such layers (1801) maybe discontinuous (e.g., islands or quantum dots) or continuous asillustrated in FIG. 1.

The epitaxial layer generally has a thickness of greater than 50 nm.Such thicknesses for the epitaxial layer may be prepared according tothe methods of the present disclosure (infra). For example, it has beenfound that such layers may be formed over a substrate from a precursorgas comprising an excess of hydrogen and a Zr, Hf, and/or Al source.

In some embodiments, the epitaxial layer may have a thickness of greaterthan about 100 nm, and preferably, greater than about 200 nm. Suchthicknesses for the epitaxial layer have been unexpectedly found to bethermally decoupled from (i.e., not thermally pinned by) the underlyingsubstrate. In contrast with epitaxial layers with thicknesses of 200 nmor less, the underlying substrate does not control the thermalproperties (e.g., coefficient of thermal expansion) of the overlyingepitaxial layer; rather, the epitaxial layer of the invention hasthermal properties, and particularly its coefficient of thermalexpansion, which are essentially similar to the bulk.

As used herein, the epitaxial layer may have a thickness of 50 nm to 2μm or 100 nm to 2 μm. In various further embodiments, the epitaxiallayer may have a thickness of 250 nm to 1.5 μm; 300 nm to 1.25 μm; 350nm to 1.25 μm; 400 nm to 1.25 μm; or 400 nm to 1 μm. In various furtherembodiments of the first aspect, the epitaxial layer may have athickness greater than 250 nm; 300 nm, 350 nm, or 400 nm. The epitaxiallayers of the invention may have any maximal thickness suitable for agiven purpose. In one embodiment, the epitaxial layer may have athickness of less than 2-3 μm; in further embodiments, the epitaxiallayer may have a thickness of less than 1.5 μm or 1 μm.

In one embodiment of the first aspect, the epitaxial layer is formeddirectly on the substrate.

In another embodiment of the first aspect, the epitaxial layer has athickness of greater than about 200 nm and has one or more of theproperties of: (i) relaxed at 900° C.; (ii) not thermally pinned to thesubstrate; (iii) a mismatch strain which is essentially thermallyconstant over a temperature range of room temperature to 900° C.; and(iv) an atomically flat surface.

In particular, the epitaxial layer formed over the substrate generallyhas an atomically flat surface over an area greater than about 50 μm².Often, the epitaxial layer has an atomically flat surface over an areagreater than about 100 μm². In a preferred embodiment, the epitaxiallayer has an atomically flat surface over an area greater than about 250μm², or 500 μm² or 1 mm². The extent of the atomically flat nature of anepitaxial layer surface can be readily determined by one skilled in theart by utilizing atomic force microscopy and XTEM techniques. Standardoptical microscopy must be use to show the absence of large islands orother imperfection in between the flat areas on the wafer surface.

In any of the preceding embodiments of the first aspect, the epitaxiallayer may comprise B and one or more elements selected from the groupconsisting of Zr, Hf and Al. In various embodiments, the epitaxial layercomprises one of ZrB₂, AlB₂, HfB₂, Hf_(x)Zr_(1−x)B₂, Hf_(x)Al_(1−x)B₂,Zr_(x)Al_(1−x)B₂, or Zr_(x)Hf_(y)Al_(1−x−y)B₂, wherein the sum of x andy is less than or equal to 1. In various further embodiments, theepitaxial layer comprises ZrB₂, HfB₂, Hf_(x)Zr_(1−x)B₂, orZr_(x)Hf_(y)Al_(1−x−y)B₂, wherein the sum of x and y is less than orequal to 1. In a further embodiment, the epitaxial layer comprises ZrB₂.

In any of the preceding embodiments of the first aspect, the epitaxiallayer is formed directly on the substrate and comprises ZrB₂,Hf_(x)Zr_(1−x)B₂, Zr_(x)Al_(1−x)B₂, or Zr_(x)Hf_(y)Al_(1−x−y)B₂, whereinthe sum of x and y is less than or equal to 1. In various furtherembodiments, the epitaxial layer is formed directly on the substrate andcomprises ZrB₂ or Hf_(x)Zr_(1−x)B₂. In a further embodiment, theepitaxial layer is formed directly on the substrate and comprises ZrB₂.

The epitaxial layer may comprise two or more epitaxial sublayers. Forexample, the epitaxial layer may comprise two epitaxial sublayers, wherethe first epitaxial sublayer is formed directly on the second epitaxialsublayer. Each of the epitaxial sublayers may comprise an alloy of B andone or more element selected from the group consisting of Zr, Hf and Al.In various embodiments, the epitaxial sublayers independently comprisean alloy of ZrB₂, AlB₂, HfB₂, Hf_(x)Zr_(1−x)B₂, Hf_(x)Al_(1−x)B₂,Zr_(x)Al_(1−x)B₂, or Zr_(x)Hf_(y)Al_(1−x−y)B₂, wherein the sum of x andy is less than or equal to 1. In various further embodiments, theepitaxial sublayer comprises ZrB₂, HfB₂, Hf_(x)Zr_(1−x)B₂, orZr_(x)Hf_(y)Al_(1−x−y)B₂, wherein the sum of x and y is less than orequal to 1.

In some embodiments, the first epitaxial sublayer is formed directly onthe substrate and comprises an alloy of ZrB₂, Hf_(x)Zr_(1−x)B₂,Zr_(x)Al_(1−x)B₂, or Zr_(x)Hf_(y)Al_(1−x−y)B₂, wherein the sum of x andy is less than or equal to 1. In this embodiment, the second epitaxialsublayer may comprise an alloy of ZrB₂, AlB₂, HfB₂, Hf_(x)Zr_(1−x)B₂,Hf_(x)Al_(1−x)B₂, Zr_(x)Al_(1−x)B₂, or Zr_(x)Hf_(y)Al_(1−x−y)B₂, whereinthe sum of x and y is less than or equal to 1. In another particularembodiment, the first epitaxial sublayer is formed directly on thesubstrate and comprises an alloy of ZrB₂, Hf_(x)Zr_(1−x)B₂,Zr_(x)Al_(1−x)B₂, or Zr_(x)Hf_(y)Al_(1−x−y)B₂, wherein the sum of x andy is less than or equal to 1 and the second sublayer comprises HfB₂. Inone particular embodiment, the first epitaxial sublayer is formeddirectly on the substrate and comprises ZrB₂ or Hf_(x)Zr_(1−x)B₂, andthe second epitaxial sublayer comprises HfB₂.

In any of the embodiments where the epitaxial layer comprises two ormore epitaxial sublayers, the epitaxial layer has a thickness of greaterthan 50 nm, 100 nm, 150 nm, 200 nm, 250 nm, 300 nm, 350 nm, or 400 nm.In another embodiment where the epitaxial layer comprises two or moreepitaxial sublayers, at least one of the epitaxial sublayers has athickness of greater than 50 nm. As used herein, the epitaxial layer mayhave a thickness of 50 nm to 2 μm, 100 nm to 2 μm, 250 nm to 1.5 μm; 300nm to 1.25 μm; 350 nm to 1.25 μm; 400 nm to 1.25 μm; or 400 nm to 1 μm.

Referring to FIG. 2, the first aspect of the invention further providesa semiconductor structure according to any of the preceding embodimentsof the first aspect, or combinations thereof, comprising a substrate(1900), a epitaxial layer having a thickness greater than 50 nm (1901),and further comprising an active layer (1902) formed over the epitaxiallayer. Such layer, (1902) may be discontinuous (e.g., islands or quantumdots) or continuous as illustrated in FIG. 2.

In one embodiment of the first aspect, the active layer (1902) islattice-matched to the epitaxial layer.

In one embodiment of the first aspect, the active layer (1902) isepitaxial.

In another embodiment of the first aspect, the active layer (1902) isformed directly on the epitaxial layer (1901).

The active region (1902) may comprise a Group III nitride. In variousembodiments, the Group III nitride comprises GaN, AlGaN, InGaN, AlInGaN,AlN, InN, SiCAlN, or mixtures thereof as well as other tetrahedralsemiconductors such as SiC and Ge.

The substrate (1800) and/or (1900) may comprise Si(e.g., p- or n-dopedSi), Al₂O₃ (e.g., sapphire), SiC or GaAs. In one embodiment, thesubstrate comprises Si(100). In another embodiment, the substratecomprises Si(111).

In another embodiment of the first aspect, the substrate comprises amiscut Si(111) wafer. While the preceding embodiments provide a path tosignificant materials improvement, it has been unexpectedly been foundthat Hf_(x)Zr_(1−x)B₂ layers with superior morphological quality can begrown directly on Si wafers that are miscut. In particular, the layersformed on miscut Si(111) wafer display incredibly flat surfaces coveringsurface areas in excess of at least 50 μm². Such surface morphologiesare highly desired for the assembly of multi-layered semiconductordevices as they lead to more highly uniform structure with lower levelsof dislocations and/or other crystalline boundaries between and withinthe individual layers, respectively.

The Si(111) wafer may be miscut by about 0.5- about 8 degrees, or about1-6 degrees, or about 2-5 degrees. In particular, when the substratecomprises a miscut Si(111) wafer, the epitaxial layer formed over thesubstrate generally has an atomically flat surface over an area greaterthan about 50 μm². Often, when the substrate comprises a miscut Si(111)wafer, the epitaxial layer formed over the substrate generally has anatomically flat surface over an area greater than about 100 μm². In apreferred embodiment, the epitaxial layer has an atomically flat surfaceover an area greater than about 250 μm², or 500 μm² or 1 mm². The extentof the flat nature of an epitaxial layer surface can be readilydetermined by one skilled in the art by, for example, optical microscopyand/or atomic force microscopy techniques.

The active layer (1902) may be formed according to methods such as, forexample, gas source molecular beam epitaxy, as is familiar to oneskilled in the art. In another embodiment, the active layer may beformed by chemical vapor deposition. Such methods are described in U.S.Patent Publication No. 2006/0236923, filed on Feb. 12, 2004, and herebyincorporated by reference in its entirety.

Methods for forming the Epitaxial Layer

In the prior art, ZrB₂ films having a thickness less than about 25-50 nmwere typically grown by gas source molecular beam epitaxy (GS-MBE) of aprecursor (Zr(BH₄)₄) at a temperature of 900° C. and a pressure of 10⁻⁷Torr. However, initial rapid growth rate studies conducted at higherpressures resulted in poisoning of the surface with B-rich fragments[possibly due to gas phase reactions of the Zr(BH₄)₄] and high surfaceroughness of approximately 20 nm.

To overcome these problems the instant invention provides a precursorgas comprising a diluent and one or more sources of B and one or moresources of Zr, Hf, and or Al. The diluent generally comprises hydrogen,and preferably, high purity hydrogen as is familiar to those skilled inthe art. As one skilled in the art would understand, a single source maycomprise both a source of B and a source of Zr, Hf, and/or Al. Forexample, Zr(BH₄)₄ and Hf(BH₄)₄ are each sources for B as well as Zr andHf, respectively. Other diluents may be used, for example, non-reactivegases such as helium and/or argon may be added to the precursor gas.

Typically, the precursor gas comprises a diluent and one or more sourcesfor the B as well as one or more sources for the Zr, Hf, and/or Al whichcomprise the epitaxial layer. Appropriate sources for the precursor gasinclude, but are not limited to Zr(BH₄)₄, Hf(BH₄)₄, and/or Al sources,such as a Knudsen cell evaporator as a source of atomic Al.Alternatively, Al(BH₄)₃-aluminum triborohydride may be used as an Alsource. The high volatility of the precursor gas component at roomtemperature (e.g., the vapor pressure of Zr(BH₄)₄ and Al(BH₄)₃ are 8Torr and 100 Torr, respectively) makes them very useful for gas sourceMBE applications. Al(BH₄)₃ thermally decomposes at the surface of asubstrate, such as Si(111), to incorporate AlB₂ in the epitaxial layerand gaseous byproducts H₂ and diborane B₂H₆ by the reaction:

2 Al(BH₄)₃→2AlB₂+B₂H₆+9H₂

In one embodiment of the invention the precursor gas comprises Zr(BH₄)₄,Hf(BH₄)₄, and/or Al(BH₄)₃ to a total volume of about 0.1 to about 5% v/vand high purity hydrogen. In a specific embodiment, the precursor gascomprises about 1 to about 3% v/v Zr(BH₄)₄, Hf(BH₄)₄, and/or Al(BH₄)₃and high purity H₂. However it will be understood, other mixing volumescan also be used, and other diluents including but not limited tohydrogen with different purity levels can also be used. Utilizing thepreceding precursor gas, films with thicknesses up to approximately 500nm, with atomically flat surfaces (e.g., surface roughness of ˜2 nm)have been obtained. Other thickness films can also be obtained as werediscussed previously (supra).

Often the excess of hydrogen comprises greater than 95% v/v of theprecursor gas; preferably, hydrogen comprises greater than 97% v/v ofthe precursor gas; even more preferably, hydrogen comprises greater thanabout 98% v/v of the precursor gas.

In embodiments of the invention, epitaxial Zr_(1−x)Hf_(x)B₂ layers havebeen synthesized across the entire compositional range (0≦x≦1), andtheir usefulness for simultaneous thermal and lattice matchingapplications has been studied.

In an embodiment of the invention, epitaxial Zr_(1−x)Hf_(x)B₂ layers maybe grown by GS-MBE using the Hf(BH₄)₄ and Zr(BH₄)₄ precursors mixed withH₂ at about 0.1 to about 5% v/v. In another embodiment of the invention,epitaxial Zr_(1−x)Hf_(x)B₂ layers may be grown by GS-MBE using theHf(BH₄)₄ and Zr(BH₄)₄ precursors mixed with H₂ at about 1 to about 3%.In another embodiment of the invention, epitaxial Zr_(1−x)Hf_(x)B₂layers may be grown by GS-MBE using the Hf(BH₄)₄ and Zr(BH₄)₄ precursorsmixed with H₂ at about 2% by volume.

The composition in an epitaxial layer of the formula, Zr_(1−x)Hf_(x)B₂,may be tuned by varying the ratio of Hf(BH₄)₄/Zr(BH₄)₄ in the stockmixture. For example, the ratio of Hf(BH₄)₄ to Zr(BH₄)₄ may be variedfrom 100:1 to 1:100, and any value in between, for example, about 1:1.

The epitaxial layer is generally formed at a temperature of about 800 to1000 degrees Celsius. Preferably, the epitaxial layer is formed at atemperature of about 850 to 950 degrees Celsius. More preferably, theepitaxial layer is formed at a temperature of about 875 to 925 degreesCelsius. Further, the precursor gas is generally provided at a pressureof about 1×10⁻³ to 1×10⁻⁹ Torr Preferably, the precursor gas is providedat a pressure of about 1×10⁻⁵ to 1×10⁻⁷ Torr

Integration of Group III Nitrides Utilizing Epitaxial Layers

The epitaxial layers described herein are particularly useful for theintegration of Group III nitride alloy layers over a substrate. Inparticular, the semiconductor structures comprising the epitaxial layersof the present invention can be used, for example, to support the growthof group III nitride materials on a substrate. The tunable structural,thermoelastic and optical properties make the HfB₂—ZrB₂ system suitablefor broad integration of III nitrides with Si.

In one non-limiting example, the buffer layer helps support growth ofgroup III nitride materials on a substrate. Such resulting semiconductorstructures having group III nitride materials can be used for activesemiconductor devices, such as transistors, field emitters,light-emitting optoelectronic devices, and optoelectronic devices.

In a third aspect, the present invention provides methods forintegrating Group III nitrides onto a substrate comprising, forming athick buffer layer of a diboride of Zr, Hf, Al, or mixtures thereof,over a substrate; and forming a Group III nitride layer over the bufferlayer. Such Group III nitrides layers, may be discontinuous (e.g.,islands or quantum dots) or continuous.

In various further embodiments of the third aspect, the buffer layer hasa thickness greater than 50 nm, 100 nm, 150 nm, 200 nm, 250 nm; 300 nm,350 nm, or 400 nm. The buffer layers of the invention may have anymaximal thickness suitable for a given purpose. In one embodiment, thebuffer layer may have a thickness of less than 2-3 μm; in furtherembodiments, the buffer layer may have a thickness of less than 1.5 μmor 1 μm.

As used herein, the buffer layer may have a thickness of 50 nm to 2 μm,100 nm to 2 μm or 200 nm to 2 μm. In various further embodiments of thethird aspect, the buffer layer may have a thickness of 50 nm to 1.5 μm;100 nm to 1.5 μm; 150 nm to 1.5 μm; 200 nm to 1.5 μm; 250 nm to 1.5 μm;300 nm to 1.25 μm; 350 nm to 1.25 μm; 400 nm to 1.25 μm; or 400 nm to 1μm.

In another embodiment of the third aspect, the buffer layer is formeddirectly on the substrate.

In another embodiment of the third aspect, the buffer layer isepitaxial.

In another embodiment of the third aspect, the buffer layer is relaxedat 900° C.

In another embodiment of the third aspect, the buffer layer has acoefficient of thermal expansion which is essentially identical to thebulk.

In another embodiment of the third aspect, the mismatch strain of thebuffer layer is essentially thermally constant over a temperature rangeof room temperature to 900° C.

In various embodiments of the third aspect, the buffer layer comprisesZrB₂, AlB₂, HfB_(2,), Hf_(x)Zr_(1−x)B₂, Hf_(x)Al_(1−x)B₂,Zr_(x)Al_(1−x)B₂, or Zr_(x)Hf_(y)Al_(1−x−y)B₂, wherein the sum of x anyy is less than or equal to 1. In a further embodiment, the buffer layercomprises ZrB₂.

In another embodiment of the third aspect, the Group III nitride layeris formed directly on the buffer layer. In yet another embodiment of thethird aspect, the Group III nitride comprises a compound selected fromthe group consisting of GaN, AlGaN, InGaN, AlInGaN, AlN, InN, SiCAlN, ormixtures thereof.

In one embodiment of the second aspect, the Group III nitride layer islattice-matched to the buffer layer.

In another embodiment of the third aspect, the substrate comprises Si,Al₂O₃, SiC or GaAs. In various embodiments of the third aspect, thesubstrate comprises Si(111). In other various embodiments of the thirdaspect, the substrate comprises Si(100). In a preferred embodiment ofthe third aspect, the substrate comprises a miscut Si(111) wafer. TheSi(111) wafer may be miscut by about 0.5- about 8 degrees, or about 1-6degrees, or about 2-5 degrees.

In another embodiment, the Group III nitride layer may be formed bymolecular beam epitaxy, as is familiar to one skilled in the art. Inanother embodiment, the Group III nitride layer may be formed bychemical vapor deposition (CVD) or metal organic chemical vapordeposition (MOCVD). Such methods are described in U.S. PatentPublication No. 2006/0236923, filed on Feb. 12, 2004, and herebyincorporated by reference in its entirety.

Methods for Forming Group III Nitride Layers

In a fourth aspect, the invention provides a method for forming anAl_(x)Ga_(1−x)N layer over a substrate comprising, contacting asubstrate with H₂GaN₃, D₂GaN₃, or mixtures thereof in the presence of anAl source at a temperature and a pressure to form a Al_(x)Ga_(1−x)Nlayer, wherein the temperature is less than about 800° C.

Without being limited by any one particular theory of operation, theformation of alloys at this temperature implies that the electron-richN₃ groups of the H₂GaN₃ or D₂GaN₃ molecule have sufficient reactivity tocombine with the acidic Al atoms to form the necessary Al—N—Ga bondingarrangements without any additional activation. The mechanism of thisinteraction may involve the formation of reactive intermediates such asthe “D₂GaN₃:Al” complex which then react on the substrate surface toyield Ga_(1−x)Al_(x)N and H₂/D₂/N₂ byproducts. In this connectionLewis-acid base type Ga—N—N—N-M bonding motifs have been observed in thestructures of molecular azides of group III compounds. At 700° C. anyGa—N—Al fragments derived from the instant decomposition of “D₂GaN₃:Al”diffuse and combine to form a uniform and continuous crystalline layer.Below this temperature elemental Al may segregate on the wafer surfacesuggesting that the “D₂GaN₃:Al” complexes disproportionate to produceclusters of elemental Al which poisons the surface and prevents anyfurther assembly of crystalline nitrides. Another competitive mechanismfor the AlGaN formation could involve the displacement of Ga withinadsorbed Ga₃N₃ units by the impinging Al atoms at the growth surface. Inthis cases since the Al—N bond is significantly stronger than the Ga—Ncounterpart the liberated Ga can diffuse on the surface and function asa surfactant to promote an organized assembly of the growing film. Itmay eventually evaporate from the growth front into the vacuum owing toits high vapor pressure at the deposition conditions (e.g., 10⁻⁷ Torrand 700° C.).

In one embodiment of the fourth aspect, the substrate is contacted withH₂GaN₃ in the presence of an Al source. In another embodiment, thesubstrate is contacted with D₂GaN₃ in the presence of an Al source. TheAl source may be any source known to those skilled in the art forsupplying elemental Al to the substrate. For example, the Al source maybe elemental Al atoms evaporated from a Knudsen cell.

Preferably, the contacting occurs at a temperature of less than about700° C., or at a temperature ranging from about 500° C. to about 700° C.The pressure for the contacting is generally ranges from about 1×10⁻⁸Torr to about 1×10⁻⁶ Torr; preferably, the pressure ranges from about2-8×10⁻⁷ Torr.

The substrate may be homogeneous, such as a Si(100) or Si(111) wafer, orcomprise one or more materials, such as one or more overlayers on a basesubstrate. For example, the substrate may comprise a buffer layer ofZrB₂ formed over a Si substrate.

In one embodiment, the substrate comprises a group III nitride, such as,but not limited to GaN. In particular, the substrate may comprise alayer of GaN formed over a base substrate, such as Si(100) or Si(111).In one embodiment, the substrate comprises a layer of GaN formed over abuffer layer (e.g.; ZrHfAlB₂) where the buffer layer is formed over abase substrate, such as Si(100) or Si(111).

The Al_(x)Ga_(1−x)N layer may be prepared according to the precedingmethods such that x has a value between 0 and 1. In a preferredembodiment, the Al_(x)Ga_(1−x)N layer thus formed has a value of xbetween about 0.01 to about 0.20; more preferably, the Al_(x)Ga_(1−x)Nlayer has a value of x between about 0.01 to about 0.10.

In various further embodiments of the fourth aspect, the Al_(x)Ga_(1−x)Nlayer may have a thickness greater than 10 nm, 25 nm, 50 nm, 100 nm, 150nm, 200 nm, 250 nm; 300 nm, 350 nm, or 400 nm. The Al_(x)Ga_(1−x)Nlayers of the invention may have any minimal or maximal thicknesssuitable for a given purpose. In one embodiment, the Al_(x)Ga_(1−x)Nlayer may have a thickness of less than 2-3 μm; in further embodiments,the Al_(x)Ga_(1−x)N layer may have a thickness of less than 1.5 μm or 1μm.

In any of the preceding embodiments of the fourth aspect, theAl_(x)Ga_(1−x)N layer is elementally homogeneous. In any of thepreceding embodiments of the fourth aspect, the Al_(x)Ga_(1−x)N layer ismonocrystalline. Preferably, in any of the preceding embodiments of thefourth aspect, the Al_(x)Ga_(1−x)N layer is epitaxial.

In any of the preceding embodiments of the fourth aspect, the substratemay comprise a semiconductor structure according to the first aspect ofthe invention.

Similarly, in any of the preceding embodiments of the fourth aspect, thesubstrate may comprise a semiconductor structure prepared according tothe second aspect of the invention.

Further, in any of the preceding embodiments of the fourth aspect, thesubstrate may comprise a semiconductor structure prepared according tothe third aspect of the invention.

Applications

The semiconductor structures of the present invention or formedaccording to the methods of the present invention may form part of anoperable microelectronic device. The semiconductor structures of anyembodiment (or combination thereof) of the second aspect may similarlyfunction as an operable microelectronic device. Further, thesemiconductor structures of any embodiment of the second aspect (orcombination thereof) may form part of an operable optoelectronic device,or itself function as an operable microelectronic device.

For example, the structures described or prepared according to themethods herein may be used in, but not limited to, heterostructure fieldeffect transistors (HFET) (see, Maeda, et al., Phys. Stat. Sol. (a) 188,No. 1, pp. 223-226 (2001), which is incorporated herein by thisreference); double heterojunction bipolar transistors, (DHBT) (see,Malcinoto, et al. Phys. Stat. Sol. (a) 188, No. 1, pp. 183-186 (2001),which is incorporated herein by this reference); multiple quantum well(MQW) lasers (see, Nakamura, et al. J. Crystal Growth 189/190, pp.841-845 (1998); and Kuramata, et al. J. Crystal Growth 189/190 pp.826-830 (1998), each of which is incorporated herein by this reference);and ultraviolet light-emitting diodes (UV LEDs) (see, Mukai, et al. J.Crystal Growth 189/190 pp. 778-781 (1998), which is incorporated hereinby this reference).

(a) Tuning Reflectivity

UV-IR ellipsometric measurements indicate that the reflectivity of pureHfB₂ is higher than that of ZrB₂, indicating that this material might besignificantly better than ZrB₂ as a reflective lattice matched templatefor nitride device fabrication on absorbing Si wafers.

The air reflectivity of pure ZrB₂ grown on Si(111) is plotted as afunction of incident photon energy in FIG. 13, where it is compared withthe reflectivity of bulk Si. The sample exhibits metallic behavior witha reflectivity increasing sharply from values near 0.5 to unity at lowphoton energy (IR region). However, in the region from 2-6 eV (620-200nm) relevant to many III-N applications the reflectivity of ZrB₂ islower than that Si.

The reflectivities of ZrB₂, HfB₂, and Si simulated from first principlesusing density functional theory (full-potential linearized augmentedplane wave method; EXCITING DFT code) illustrate the ability of theZrB₂—HfB₂ system to tune the optical properties of buffer layers on Si.For more information about the code, see J. K. Dewhurst, S. Sharma andC. Ambrosch-Draxl, EXCITING FPLAPW code Version 0.9.57 (2006),incorporated herein by reference.

Due to the semi-metallic character of the compounds the complexdielectric function ε=ε₁+iε₂ was calculated as the sum of interband andintraband contributions. (See C. Ambrosch-Draxl and J. O. Sofo, Comp.Phys. Comm. 175, 1 (2006), incorporated herein by reference. The latterare described using Drude expressions

ε₁ ^(INTRA)=1−ω_(p) ²/(ω² +iωΓ)

where ωp is the free-electron plasma frequency (calculated values areωP=4.56 and 4.81 eV for ZrB₂ and HfB₂, respectively). A lifetimebroadening value of Γ=50 meV was found to reproduce the observed lowenergy behavior. The steep rise observed in IR reflectivities of bothHfB₂ and ZrB₂ is due to the Drude term.

The close agreement between the observed and simulated spectra for Siand ZrB₂ suggests that the reflectivity of pure HfB₂ films should beabout 20% larger than that of ZrB₂ in the 2-8 eV range.Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1, 0≦y≦1) materials grown on Si can offertunable reflectivities across the entire spectral range. This behaviorcan be of particular significance for the design of nitride basedinterband (near-IR) and intersub-band (IR) devices grown on buffered Si.

In a fifth aspect, the invention provides a method for tuning thereflectivity of a buffer layer comprising, forming a buffer layer of analloy of the formula Hf_(x)Zr_(1−x)B₂ having a thickness greater thanabout 50 nm and a reflectivity over a substrate, wherein x is apredetermined value from 0 to 1, and wherein the reflectivity of thebuffer layer is greater than a layer of ZrB₂ having an identicalthickness as the buffer layer.

In various embodiments of the fifth aspect, the buffer layer may have athickness greater than 50 nm, 100 nm, 150 nm, 200 nm, 250 nm; 300 nm,350 nm, or 400 nm. The buffer layer of the invention may have anyminimal or maximal thickness suitable for a given purpose. In oneembodiment, the buffer layer may have a thickness of less than 2-3 μm;in further embodiments, the buffer layer has a thickness of less than1.5 μm or 1 μm.

In one embodiment, a semiconductor structure is provided comprising asubstrate, a buffer layer comprising Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1,0≦y≦1) formed over the substrate, and an active layer formed over thesubstrate, wherein the active layer is lattice matched to the bufferlayer.

In another embodiment, a semiconductor structure is provided comprisinga substrate, a buffer layer comprising Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1,0≦y≦1) formed over the substrate, and an active layer formed over thesubstrate, wherein the active layer is relaxed.

In another embodiment, a semiconductor structure is provided comprisinga substrate, a buffer layer comprising Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1,0≦y≦1) formed over the substrate, and an active layer formed over thesubstrate, wherein the active layer is relaxed and lattice matched tothe buffer layer

In any of the preceding embodiments, the active layer may comprise aGroup III nitride. For example, the Group III nitride may comprise AlGaNor GaN. In one embodiment, the Group III nitride may compriseAl_(x)Ga_(1−x)N, wherein x is greater than about 0.10.

In various embodiment, the substrate comprises Si(111). In other variousembodiments, the substrate comprises Si(100). In a preferred embodiment,the substrate comprises miscut Si(111); preferably, the substratecomprises a miscut Si(111) wafer. The Si(111) wafer may be miscut byabout 0.5- about 8 degrees, or about 1-6 degrees, or about 2-5 degrees.

(b) Tuning Lattice Constant

Alloys of ZrB₂, with bulk hexagonal lattice constants a₀=3.169 Å,c₀=3.525 Å, and HfB₂ (a₀=3.142 Å and c₀=3.48 Å) have lattice constantssmaller than those of ZrB₂, and therefore make it possible to growhigher Al content Al_(x)Ga_(1−x)N layers with less strain, paving theway towards full integration of these materials with substrates such asSi.

A hybrid substrate technology (based on alloys of ZrB₂ and the HfB₂) hasbeen developed that extends the lattice matching capability on siliconfor growth of wider band gap Al_(x)Ga_(1−x)N with x>0.10. Solidsolutions of Zr_(1−x)Hf_(x)B₂ possess tunable lattice constants lowerthan that of ZrB₂, well within the Al_(x)Ga_(1−x)N range of interest.

In a sixth aspect, the invention provides a method for tuning thelattice constant of a buffer layer comprising, forming a buffer layer ofan alloy of the formula Hf_(x)Zr_(1−x)B₂ having a thickness greater thanabout 50 nm, and forming an active layer over the buffer layer, whereinx is a predetermined value from 0 to 1, and wherein the active layer islattice matched to the buffer layer.

In various embodiments of the sixth aspect, the buffer layer may have athickness greater than 50 nm, 100 nm, 150 nm, 200 nm, 250 nm; 300 nm,350 nm, or 400 nm. The buffer layer of the invention may have anyminimal or maximal thickness suitable for a given purpose. In oneembodiment, the buffer layer may have a thickness of less than 2-3 μm;in further embodiments, the buffer layer may have a thickness of lessthan 1.5 μm or 1 μm.

In one embodiment, a semiconductor structure is provided comprising asubstrate, a buffer layer comprising Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1,0≦y≦1) formed over the substrate, and an active layer formed over thesubstrate, wherein the active layer is lattice matched to the bufferlayer.

In another embodiment, a semiconductor structure is provided comprisinga substrate, a buffer layer comprising Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1,0≦y≦1) formed over the substrate, and an active layer formed over thesubstrate, wherein the active layer is relaxed and lattice matched tothe buffer layer

In any of the preceding embodiments, the active layer may comprise aGroup III nitride. For example, the Group III nitride may comprise AlGaNor GaN. In one embodiment, the Group III nitride may compriseAl_(x)Ga_(1−x)N, wherein x is greater than about 0.10.

In various embodiment, the substrate comprises Si(111). In other variousembodiments, the substrate comprises Si(100). In a preferred embodiment,the substrate comprises miscut Si(111); preferably, the substratecomprises a miscut Si(111) wafer. The Si(111) wafer may be miscut byabout 0.5- about 8 degrees, or about 1-6 degrees, or about 2-5 degrees.

(c) Distributed Bragg Reflectors and Superlattices

It will also be understood that buffer layer in the precedingdescription of the invention may include more than two different layertypes, wherein each layer type is periodically repeated through asuperlattice. Thereby, in a seventh aspect, the invention provides asemiconductor structure comprising, a stack comprising a plurality ofrepeating alloy layers, formed over a substrate, wherein the repeatingalloy layers comprise two or more alloy layer types, wherein at leastone alloy layer type comprises a Zr_(z)Hf_(y)Al_(1−z−y)B₂, alloy layer,wherein the sum of z and y is less than or equal to 1, and the thicknessof the stack is greater than about 50 nm.

Referring to FIG. 25, an exemplary embodiment of the seventh aspect isillustrated using two layer types for simplicity and ease of discussion.Buffer region 104 may be about 50 nm to 1000 nm or 100 nm to 1000 nmthick, although thicker layers may also be grown, whereas the thicknessof individual layers (e.g., t₂₀₂ and t₂₀₄) may be of the order ofseveral nanometers or tens of nanometers (e.g., 5 nm to 50 nm).

Generally, when the stack comprises two types of alloy layers, A and B,respectively, the stack comprises a structure of the form -(AB)_(n)-,where n is greater than or equal to 1; when the stack comprises threetypes of alloy layers, A, B, and C, respectively, then stack comprises astructure of the form -(ABC)_(n)-, -(BAC)_(n)-, -(ACB)_(n)-,-(BCA)_(n)-,-(CBA)_(n)-, or -(CAB)_(n)-,where n is greater than or equalto 1. Preferably, n is about 1 to 100; more preferably, n is about 1 to50; even more preferably, n is about 1 to about 10.

When the stack comprises four types of alloy layers, A, B, C, and D,respectively, then stack may comprises, for example, a structure of theform -(ABCD)_(n)-, -(ABDC)_(n)-, -(ACBD)_(n)-, -(ACDB)_(n)-,-(ADBC)_(n)-, -(ADCB)_(n)-, -(BACD)_(n)-, -(BADC)_(n)-, -(BCAD)_(n)-,-(BCDA)_(n)-, -(BDAC)_(n)-, -(BDCA)_(n)-, -(CABD)_(n)-, -(CADB)_(n)-,-(CBAD)_(n)-, -(CBDA)_(n)-, -(CDAB)_(n)-, -(CDBA)_(n)-, -(DABC)_(n)-,-(DACB)_(n)-, -(DBAC)_(n)-, -(DBCA)_(n)-, -(DCAB)_(n)-, or-(DCBA)_(n)-,Preferably, n is about 1 to 100; more preferably, n is about 1 to 50;even more preferably, n is about 1 to about 10.

Additionally, knowledge of the dielectric functions and reflectivitiesof Zr_(x)Hf_(y)Al_(1−x−y)B₂ allows the design of buffers with tailoredreflectivities. Design rules for structures with tailoredreflectivities, such as Distributed Bragg Reflectors (DBRs),anti-reflection coatings and the like are described by Hecht in “Optics(4th Edition)”, Addison Wesley Publishing Company, 2002, incorporatedherein by reference. A DBR mirror structure consists of alternate layersof materials with different refractive indices. The optical thickness ofeach layer is one quarter of the design wavelength—that is, thewavelength for which the reflector is designed to have high reflectivity(also referred to as center wavelength). Physically, the thickness of aDBR layer for a DBR designed for a center wavelength lambda (λ) is givenby t=λ/4n where n is the refractive index of the material at thewavelength λ. At this wavelength, the partial waves reflected at theinterfaces between these layers interfere constructively, resulting in avery high reflectance within a narrow spectral region. The reflectivityspectrum has a center wavelength (λ) and a wavelength range either sidewhere the reflectivity can be high. The magnitude of the reflection at agiven wavelength, and the wavelength dependency of the reflectivityspectrum are determined by the refractive index difference between thetwo materials, and the number of layers forming the mirror structure.Thus it is possible to design a buffer layer that can be epitaxiallygrown on a substrate to have a high reflectivity that can be used by thenitride device formed on the buffer.

The substrate may comprise Si, Ge, SiGe, Al₂O₃, SiC or GaAs. In variousembodiments of the sixth aspect, the substrate comprises Si(111). Inother various embodiments of the seventh aspect, the substrate comprisesSi(100). In a preferred embodiment of the seventh aspect, the substratecomprises miscut Si(111). In a preferred embodiment of the seventhaspect, the substrate comprises a miscut Si(111) wafer. The Si(111)wafer may be miscut by about 0.5- about 8 degrees, or about 1-6 degrees,or about 2-5 degrees, or about 4 degrees.

Each of the plurality of repeating alloy layers may have a thicknessranging from about 2 nm to about 500 nm. Preferably, each repeatingalloy layer has a thickness ranging from about 5 to 100 nm or from about100 nm to about 500 nm.

The thickness of the stack is generally greater than about 50 nm, 100nm, 200 nm, 300 nm, 400 nm or 500 nm. More specifically, the stack mayhave a thickness of about 50 nm to about 1000 nm, about 100 nm to about1000 nm, or about 250 nm to 1.5 μm; 300 nm to 1.25 μm; 350 nm to 1.25μm; 400 nm to 1.25 μm; or 400 nm to 1 μm. The stack of the invention mayhave any maximal thickness suitable for a given purpose. In oneembodiment, the stack has a thickness of less than 2-3 μm; In furtherembodiments, the stack layer may have a thickness of less than 1.5 μm or1 μm.

The semiconductor structure of the seventh aspect may further comprisean active layer, as defined herein, formed over the stack. In oneembodiment, the active layer is formed directly on the stack. In anotherembodiment, the stack is formed directly on the substrate. In yetanother embodiment, the active layer is formed directly on the stack andthe stack is formed directly on the substrate. In such embodiments, theactive layer may comprise a Group III alloy, for example, GaN, AlGaN,InGaN, AlInGaN, AlN, or InN. In other embodiments, the active layer maycomprise an alloy of SiCAlN or SiC. In another embodiment, the activelayer may comprise Ge.

Each of the layers in the stack, as well and the active layer, whenpresent, may be formed according to any of the methods described herein,or according to those methods known to those skilled in the art, forexample, molecular beam epitaxy, chemical vapor deposition, orsputtering. In general, it is preferred that each of the plurality oflayers in the stack of the seventh aspect is epitaxial; preferably, theentire stack is epitaxial.

Definitions

The term “epitaxial” as used herein, means that a material iscrystalline and fully commensurate with the substrate. Preferably,epitaxial means that the material is monocrystalline, as defined herein.

The term “monocrystalline” as used herein, means a solid in which thecrystal lattice of the entire sample is continuous with no grainboundaries or very few grain boundaries, as is familiar to those skilledin the art.

The term “flat surface” when used in reference to a layer as used hereinmeans the layer has a surface roughness which is less than about 5% thelayer thickness. For example, a 100 nm layer is atomically flat when thelayer has a surface roughness of less than 5 nm. The term refers to theexposed surface of the referenced layer which is generally normal to thegrowth direction of the layer, as would be understood by one skilled inthe art.

The terms “thick film” and “thick layer” as used herein mean a film orlayer having an average thickness of greater than 100-200 nm; in variousfurther embodiments, a thick film or layer has an average thickness ofat least 250 nm, 300 nm, 350 nm, or 400 nm. Thick films and layers asused herein can have any maximal thickness suitable for a given purpose.In one embodiment, a thick film or layer has a thickness of less than2-3 μm; in various further embodiments, a thick film or layer has athickness of less than 1.5 μm, 1.25 μm, or 1.0 μm.

Typically, as used herein, “thick films” and “thick layers” have athickness of 100 nm to 2 μm. In various further embodiments, a thickfilm or layer has a thickness of 150 nm, 200 nm, or 250 nm to 2 μm, 300nm-2 μm, 350 nm-2 82 m, 400 nm-2 μm, 250 nm-1.5 μm, 300 nm-1.5 μm,350-1.5 μm, 400 nm-1.5 μm, 250 nm-1.25 μm, 300 nm-1.25 μm, 350-1.25 μm,400 nm-1.25 μm, 250 nm-1 μm, 300 nm-1 μm, 350-1 μm, or 400 nm-1 μm.

The term “thermally pinned” as used herein, means that the rate ofthermal expansion for a material on a substrate, i.e. its coefficient ofthermal expansion, essentially matches that of the substrate and therate of thermal expansion for the material on the substrate differs fromits rate of thermal expansion for the bulk material. (i.e., thesubstrate and the film expand at the same rate).

The term “mismatch strain” as used herein, means the strain induced in amaterial layer formed over a substrate by the differences in the latticeconstants of the material and substrate.

The term “essentially thermally constant” as used herein, means that thereferenced item changes less than 10% over the specified temperaturerange. Preferably, the referenced item changes less than 5% over thetemperature range.

The term “lattice-matched” as used herein, means the lattice constantsof the referenced materials differ by less than about 1%. (i.e., thelattice mismatch is less than about 1%).

It should be understood that when a layer is referred to as being “on”or “over” another layer or substrate, it can be directly on the layer orsubstrate, or an intervening layer may also be present. It should alsobe understood that when a layer is referred to as being “on” or “over”another layer or substrate, it may cover the entire layer or substrate,or a portion of the layer or substrate.

It should be further understood that when a layer is referred to asbeing “directly on” another layer or substrate, the two layers are indirect contact with one another with no intervening layer. It shouldalso be understood that when a layer is referred to as being “directlyon” another layer or substrate, it may cover the entire layer orsubstrate, or a portion of the layer or substrate.

EXAMPLES Example 1 Preparation of the Epitaxial ZrB₂ Layers

Thick, monocrystalline ZrB₂ layers (up to 500 nm thick) were grown onthe Si(111) hexagonal surface at a temperature, pressure and reactantconcentration of 900° C., 2-4×10⁻⁶ Torr and ˜1% Zr(BH₄)₄/H₂,respectively. The reaction mixture based on 4 Torr/liter of Zr(BH₄)₄ anda large excess of research grade H₂ was prepared prior to eachdeposition by combining the pure compounds in a 1000 mL vacuum flask attotal final pressure of 400 Torr. The flask was connected to the gasinjection manifold of the deposition chamber, and the manifold waspumped to ˜10⁻⁸ Torr. A boron doped (1-10 Ω-cm), Si(111) wafer wascleaved to 1 cm² size substrates to fit the dimensions of the samplestage. Each substrate was sonicated in methanol for 5 minutes, driedunder a stream of purified N₂, inserted through a load lock into thegrowth chamber at a base pressure of 4×10⁻¹⁰ Torr, and heated at 600° C.under UHV to remove surface contaminants until the pressure of thechamber was restored to background levels. The wafer was thensubsequently flashed at 1150° C. five times to desorb the native oxidefrom the surface. To commence film growth, the wafer was heated to 900°C. by passing direct current though it. The temperature was measuredwith a single-color pyrometer and allowed to stabilize for 5 minutes.The precursor mixture was introduced into the chamber at a constant flowrate of ˜0.08 sccm, controlled by a manual leak valve. The reactionpressure inside the chamber was maintained between 2×10⁻⁶ and 2×10⁻⁵Torr during growth by dynamic pumping using a corrosion resistantturbomolecular pump. The growth conditions were judiciously tuned in amanner that follows a perfect decomposition mechanism according to thereaction,

Zr(BH₄)₄→ZrB₂+B₂H₆+5H₂.

The resulting ZrB₂ on Si films grew at a rate of up to 1 nm/min,yielding thicknesses up to 500 nm.

Very slowly cooling the samples from 900° C. to room temperature overthe course of 30 minutes can avoid cracking of the layers (depending onthickness) due to the difference in thermal expansion between the ZrB₂material and the Si substrate.

Example 2 Structural and Morphological Characterization of EpitaxialZrB₂ Layers

The resultant films of Example 1 are fully commensurate and perfectlyoriented with the underlying hexagonal surface as evidenced by variousmicrostructural and surface characterization techniques includingRutherford backscattering (RBS) ion channeling, atomic force microscopy(AFM) and transmission electron microscopy (XTEM) (see FIG. 3). Thelatter reveals that heteroepitaxy between ZrB₂(0001) and Si(111) isobtained via coincidence-misfit mechanism in which five lattice rows ofSi are aligned with every six rows of ZrB₂, (i.e., “magic mismatch”).This registry results in a periodic array of edge dislocations along theinterface which accommodate the large difference in lattice constants.

As mentioned above it is extremely critical to maintain the optimalgrowth conditions and any deviations, however minor, invariably resultin either negligible growth of crystalline material or in the formationof polycrystalline grains with inferior morphologies. The visualappearance of the films is metallic and reminiscent of aluminum mirrors,particularly for samples ˜400-500 nm thick. Scanning electron microscopyimages of the ZrB₂ films in plan view and cross sectional geometriesappeared to be featureless and devoid of fractures or surface cracks.AFM scans showed that the film surface is dominated by an array ofshallow undulations with variable lateral extent in the range from 1-2microns in diameter. Their corresponding heights are found to bedependent on the film thickness and span 2 to 5 nm for samples withthickness 100 to 500 nm, respectively. The three dimensional habit ofindividual undulations resembles a hexagonal shaped pyramid with a verysmall aspect ratio. The vertical distance from the base to the apex isapproximately 2-5 nm as determined by AFM measurements (RMS roughness).The surface structure suggests that the growth proceeds via formation oflarge columnar grains which terminate in pyramidal shaped apices. Theconvex surface portion of these features is comprised of stackedhexagonal mesas with progressively decreasing diameters. This morphologyis consistent with layer-by-layer growth on the μm scale within eachgrain.

Example 3 High Resolution XRD Film Strain Studies of Epitaxial ZrB₂Layers

The structural quality and crystallographic orientation of these thickfilms of Example 1 were analyzed by high resolution x-ray diffraction(HR-XRD) using a Panalytical X-pert Pro diffractometer. The θ-2θ scansrevealed only the (001) and (002) peaks of the hexagonal lattice,indicating that the heterostructure is highly oriented and epitaxial.The double crystal rocking scans of ZrB₂(001) showed full width at halfmaxima (FWHM) of 0.15 degrees for 500 nm thick films, indicating nosignificant tilt between the crystalline domains, consistent withextremely narrow mosaicities within the horizontal direction. Forsamples with a nominal thickness up to 100 nm a symmetrical envelope ofinterference fringes is also present in the vicinity of the ZrB₂ peak inthe θ-2θ diffraction patterns. For higher thickness samples thesefringes merge within the parent (001) peak.

Extensive off-axis high-resolution measurements were also performed todetermine the precise in-plane and vertical lattice parameters and tofollow the evolution of the lateral strain as a function of filmthickness and temperature. For this purpose, the (113) reciprocal spacemaps (RSM) of the ZrB₂ crystal (AlB₂-type structure) were recorded owingto its relatively high intensity and geometric accessibility within thescattering configuration of our diffraction apparatus. Routine andreproducible sample alignment was carried out using the (224) reflectionof the Si(111) wafer as a reference point due to its close proximity inreciprocal space to the epilayer (113) peak. For a typical 500 nm thickZrB₂/Si(111) a detailed analysis of the reciprocal space maps at roomtemperature yielded correlation lengths of ˜0.5 μm and angular tiltbetween adjacent grains of ˜658 arcseconds indicating that this materialis of high crystalline quality Similar values are obtained for all filmsstudied irrespective of their thickness. The measured lattice parametersfor this sample, a=3.1857 Å and c=3.5212 Å, were found to be slightlydifferent than the relaxed bulk ZrB₂ values a₀=3.169 Å, c₀=3.530 Å (see,Okamoto, et al., J. Appl. Phys. 93, 88 (2003)), indicating that the filmis tensile strained. As shown below, the strain value obtained fromstandard elasticity theory is approximately 0.5%.

The design of template structures based on ZrB₂ layers grown on Sirequires a thorough understanding of the thickness and temperaturedependence of the strain in the system. The variation of the strain as afunction of epilayer thickness at room temperature were determined viameasurement of high resolution XRD reciprocal space maps of the (113)diffraction maxima for a series of films with thicknesses in the rangeof 50-500 nm. In order to accurately evaluate the in-plane strain ofthese ZrB₂ films the measured a and c lattice constants were used tocalculate the dimensions of the relaxed unit cell for each thickness.For hexagonal films with the [0001] plane oriented normal to thesubstrate surface, the perpendicular (ε_(c)) and parallel (ε_(a))strains are given by ε_(c)=−2C₁₃ε_(a)/C₃₃ where ε_(c)=(c-c₀)/c₀ andε_(a)=(a-a₀)/a₀. For bulk ZrB₂ the known c/a ratio (denoted by η below)is 1.1139. The room temperature elastic constants are C₁₃=120.5 GPa andC₃₃=436.1 GPa, yielding ξ=−2C₁₃/C₃₃=−0.553. From inversion of the strainrelation the relaxed lattice constants are then given bya₀={c/η−ξa}/{1−ξ} and c₀=η a₀, and these are listed in Table 1 togetherwith the experimental values.

The relaxed lattice parameters a₀ and c₀ of the 50-500 nm thick ZrB₂layers were derived using an approximation that η for the relaxedepitaxial film is identical to that of the equilibrium bulk crystals.The computed strains states of the films are given in parentheses nextto the measured a and c values in Table 1.

The relaxed lattice constants of the films were calculated to bevirtually the same and match the known values for the bulk phasea₀=3.169 Å and c₀=3.530 Å. This finding demonstrates the remarkableconsistency of the in-plane strain determination and shows that thelattice parameters are accurate to ˜0.001 Å. Strain analysis also showsthat all ZrB₂ films with thicknesses larger than 50 nm exhibit a tensilestrain with average value of ε_(a)˜+0.51% and ε_(c)˜−0.30%. The tensilestrain does not change with increasing thickness up to 500 nm at roomtemperature. The residual strains were found to be remarkably robusteven after the films were heated either via rapid-thermal-annealing forseveral seconds up to 1100° C., or by post growth treatments under UHVconditions for up to 24 hours at 900° C.

The fact that all of the ZrB₂ films considered were found to be tensilestrained has significant implications for the use of these materials asbuffer layers for nitride integration with Si. The average measuredvalue of a at room temperature is essentially identical to that of GaN(a=3.189 Å) indicating that these buffers might be suitable platformsfor integration of nitrides on Si.

However, for this strategy to succeed a thorough understanding of theevolution of strain in the ZrB₂ films with temperature is also required.The need for such a study is underscored by the following observation:if we assume that the ZrB₂ films are relaxed at the growth temperatureof 900° C. and track the Si substrate (expand at the same rate) whencooling from the growth temperature, we can use the measuredcoefficients of thermal expansion (CTE) for bulk ZrB₂ (α_(a) for thebasal dimension) and bulk Si(α) to predict the strain at roomtemperature. Using α_(a)=6.66×10⁻⁶ K⁻¹ for ZrB₂ (Okamoto, et al., J.Appl. Phys. 93, 88 (2003)), and α=3.78×10⁻⁶ K⁻¹ for Si, however, wepredict a strain ε_(a) (20° C.) ˜0.2% which is much smaller than the˜0.5% values observed in our samples (Table 1). In the context of thisdiscrepancy our ZrB₂/Si(111) epitaxial system appears to exhibit adifferent behavior in comparison to typical compliant film systems grownepitaxially on mismatched substrates, i.e., Ge grown on Si.

One distinction which may account for the higher than expected tensilestrain (˜0.5%) and its thickness independence at room temperature isthat the stiffness of the ZrB₂ epilayer is much greater than that of theSi substrate. Furthermore, at the high growth temperatures the presentstudy (900° C.) the silicon substrate becomes far less mechanicallyrigid. The large differences in the elastic and thermal properties ofZrB₂ and Si are therefore likely to produce complicated and perhapsunexpected strain response in the heterostructure, particularly sincethe synthesis involves large variations in temperature (e.g., ΔT˜900°C., compared to ΔT˜400° C. in conventional semiconductor applications).

To elucidate the origin of this residual strain, a study of the thermalbehavior was undertaken using representative ZrB₂/Si samples withthicknesses of 200 and 400 nm, intermediate among those shown onTable 1. If the room-temperature strain in these samples is controlledby the thermal expansion differential between the ZrB₂ and Si uponcooling, then the above discussion implies that there must be anon-vanishing strain at the growth temperature. This strain would likelybe associated with the registry at the interface (coincidence of 6 ZrB₂with 5

TABLE 1 Measured lattice parameters a and c as a function of thickness hat room temperature. The corresponding lattice parameters a₀ and c₀ werecalculated using η = 1.1139 and the observed⁸ value ξ = −0.553, yieldingthe strain values listed in parentheses. h (nm) a₀ (Å) c₀ (Å) a (Å) (%strain) c (Å) (% strain) 50 3.171 3.532 3.1886 (0.57%) 3.5206 (−0.31%)110 3.170 3.531 3.1862 (0.52%) 3.5208 (−0.29%) 150 3.170 3.531 3.1856(0.51%) 3.5206 (−0.28%) 170 3.170 3.531 3.1870 (0.55%) 3.5201 (−0.30%)380 3.169 3.530 3.1849 (0.49%) 3.5209 (−0.27%) 400 3.169 3.530 3.1858(0.52%) 3.5201 (−0.29%) 500 3.170 3.531 3.1857 (0.50%) 3.5212 (−0.28%)Si lattice rows [see, Hu, et al. J. Cryst. Growth 267 (3-4), 554-563(2004); Tolle, et al., Appl. Phys. Lett. 84 (18), 3510-3512 (2004)]established within the first few nanometers of growth, and would becomeimmutably fixed no matter how thickly the film is subsequently grown.Sufficiently thick films might be expected to display a vanishing strain(full relaxation) at the growth temperature. This study demonstratesthat both mechanisms are in operation.

A thinner (200 nm) sample was heated to a series of temperatures in therange of 20-900° C. and the corresponding lattice parameters wererecorded at each temperature using the diffractometer's Anton Paar hightemperature stage capable of reaching 900° C. The heating was conductedunder inert atmosphere conditions in a dynamic flow of UHP nitrogen at a4 psi overpressure to avoid oxidation of the samples. At eachtemperature the film was realigned using the Si(224) reflection tocorrect for any sample drift associated with the diffractometer stageexpansion. The lattice parameters of the boride film were determinedfrom measurements of the off-axis ZrB₂ (113) reciprocal space maps(RSM).

Table 2 lists the temperature dependence of the observed film latticeparameters, a and c for ZrB₂, the corresponding lattice constant a forSi, the calculated relaxed values a₀(T) and c₀(T), and the associatedstrains ε_(∥)(T) and ε_(⊥)(T) obtained from the analysis. The latterwere obtained using the same formalism as described above in the contextof the thickness dependence of the film strain. The c/a ratio, η(T), ofa fully relaxed ZrB₂ film was assumed to be the same as that of acorresponding equilibrium bulk ZrB₂ crystal at any given temperature.The variation of η(T) with temperature was obtained from the recentlymeasured CTE for bulk ZrB₂ (including the temperature dependence of theCTE itself). The temperature dependence of the elastic ratio,ξ(T)=−2C₁₃(T)/C₃₃(T), was also obtained from recent measurements of theelastic constants C₁₃(T) and C₃₃(T) for bulk ZrB₂ crystals (Okamoto, etal. J. Appl. Phys. 93, 88 (2003)), assuming that the strain relationε_(⊥)(T)=ξ(T)ε_(∥)(T) remains valid over the temperature range of ourstudy (20-900° C.).

TABLE 2 Thermal analysis of the 200 nm thick ZrB₂ film on Si(111).Measured values of a and c for ZrB₂ and a(Si) are listed in bold font.The relaxed lattice constants. a₀ and c₀, at each temperature wereobtained from a strain analysis using the known temperature dependenceof bulk ZrB₂ elastic constants and that of the equilibrium bulk c/aratios (as described in the text). Also listed is the temperaturedependence of the Si lattice constant which is well-described by aconstant linear CTE FILM BULK T (° C.) a (Si) a^(FIT) (Si) ξ (T) η (T)a₀ (Å) c₀ (Å) a (Å) (% strain) c (Å) (% strain) F (%) F₀ (%) 20 5.43085.4308 −0.553 1.11392 3.1690 3.5300 3.1835 (0.46%) 3.5212 (−0.25%) 0.5250.983 200 5.4339 5.4343 −0.557 1.11400 3.1728 3.5345 3.1876 (0.47%)3.5253 (−0.26%) 0.450 0.933 500 5.4404 5.4404 −0.566 1.11413 3.17963.5425 3.1922 (0.40%) 3.5346 (−0.22%) 0.425 0.850 700 5.4449 5.4445−0.572 1.11422 3.1838 3.5475 3.1942 (0.33%) 3.5408 (−0.19%) 0.442 0.792900 5.4506 5.4485 −0.578 1.11431 3.1883 3.5527 3.1965 (0.26%) 3.5474(−0.15%) 0.475 0.733Table 2 also lists the coincidence lattice misfit F introduced byMatthews,.(see, Matthews, Report No. RC 4266 No. 19084, 1973; R. W.Vook, International Metals Reviews 27 (4), 209-245 (1982); K. H. PloogA. Trampert, Crystal Research and Technology 35 (6-7), 793-806 (2000))which the present case is defined asF=(5d_(Si—Si)-6a_(ZrB2))/(6a_(ZrB2)), where d_(Si—Si)=a_(Si)/√{squareroot over (2)} is the Si—Si distance in the (111) plane. F₀ denotes thecoincidence misfit calculated with bulk ZrB₂ parameters. From thedefinition it is clear that F+ε_(a)=F₀. This bulk coincidence misfit F₀was calculated using thermal expansion data from Okamoto (J. Appl. Phys.93, 88 (2003)), and has a room temperature value of 0.983%, which meansthat the ZrB₂ basal lattice parameter is slightly less than required fora perfect 6/5 coincidence. At the growth temperature of 900° C. themisfit decreases to a value of 0.733%, since the CTE of Si is smallerthan that of the basal plane of ZrB₂. At this temperature the basalplain strain is ε_(a)=0.26%, which means that 35% of the coincidencemisfit is taken up by tensile strain in the ZrB₂ film. The remaining 65%is thus accommodated by additional misfit dislocations or by strainingthe interfacial region. Upon cooling to room temperature the coincidencemisfit remains essentially constant, indicating that the rate ofcontraction of the ZrB₂ film in the basal plane matches that of theunderlying Si.

The tracking behavior can be clearly seen in the temperature dependenceof the strain in the 200 nm thick film which is presented graphically inFIG. 4. The lines represent the predicted trend assuming measuredstrains at the growth temperature and a ZrB₂ a-axis thermal expansionequal to that of the underlying Si. The agreement is excellent,confirming that the higher than expected tensile strain observed at roomtemperature (˜0.5%) is due to a tensile strain ε_(a)=0.26% alreadypresent at the growth temperature.

Combined with the observation that all samples produced in the thicknessdependence study (Table 1) have approximately the same value of tensilestrain (0.5%) at room temperature, suggests that all films should alsohave the same value of strain ˜0.26% at the growth temperature. Howeverthis appears to contradict the expectation that the strain in the thickbulk-like ZrB₂ films must also eventually vanish with increasingthickness.

To further elucidate the strain status of ZrB₂ films as a function ofthickness both at their growth temperature and upon cooling, and resolvethe above issues, the 200 nm film temperature study was repeated for athicker 400 nm sample. The results are shown in Table 3 and alsographically in FIG. 5.

While a residual strain of ˜+0.26% was observed in the basal plane inthe 200 nm film at the growth temperature of 900° C., the correspondingstrain essentially vanishes in the 400 nm film described in Table 3.FIG. 5 compares the observed data (symbols) with the predicted trend(lines) assuming zero strain at the growth temperature and a ZrB₂ a-axisthermal expansion equal to that of the underlying Si for the 400 nmthick sample. The comparison shows that the strain in both a and c islarger than expected, which indicates that the ZrB₂ is not thermallypinned to the underlying Si.

In the case of the 200 nm thick film (see FIG. 4) the temperaturedependence of the strain followed this model precisely, indicating thatthe epilayer and Si expand at the same rate. Thus, the most significantdistinction between the thermal behavior of the thin and thick ZrB₂films is that thin 200 nm sample tracks the Si but the 400 nm thicksample does not. This in turn implies the existence of a“pseudo-critical” thickness in the range of 200-400 nm, at the growthtemperature 900° C.

TABLE 3 Thermal analysis of the 400 nm thick ZrB₂ film on Si(111)showing the same parameters as in Table 2. Note that small residualstrain essentially vanishes at the growth temperature of 900° C., incontrast with the residual strain of 0.26% found for the 200 nm sample(Table 2). FILM BULK T (° C.) a (Si) a^(FIT) (Si) ξ (T) η (T) a₀ (Å) c₀(Å) a (Å) (% strain) c (Å) (% strain) F (%) F₀ (%) 20 5.4307 5.4307−0.553 1.11392 3.1692 3.5302 3.1843 (0.48%) 3.5209 (−0.26%) 0.491 0.983200 5.4338 5.4343 −0.557 1.11397 3.1729 3.5345 3.1850 (0.38%) 3.5270(−0.21%) 0.533 0.933 400 5.4378 5.4384 −0.563 1.11403 3.1779 3.54033.1859 (0.25%) 3.5353 (−0.14%) 0.575 0.875 600 5.4422 5.4425 −0.5691.11409 3.1816 3.5445 3.1868 (0.16%) 3.5412 (−0.09%) 0.625 0.812 8005.4466 5.4466 −0.575 1.11415 3.1857 3.5493 3.1879 (0.07%) 3.5479(−0.04%) 0.675 0.758 900 5.4488 5.4486 −0.578 1.11418 3.1877 3.55173.1887 (0.03%) 3.5511 (−0.02%) 0.691 0.733

To verify that these puzzling results are not due to phaseinhomogeneities in the thick film samples or to measurement errors, FIG.6 shows the measured a and c parameters for the 400 nm film, thecalculated relaxed values a₀ and c₀, and the lattice parameters (solidlines) for bulk ZrB₂ as a function of temperature. As in the case of the200 nm sample, the agreement between the relaxed parameters for the 400nm sample and the bulk values is excellent, confirming that the thermalbehavior of the film should be understandable in terms of the elasticproperties of standard ZrB₂ crystals.

The observation of virtually no strain at the growth temperaturesuggests a bulk-like behavior for thicker samples. However, if the 400nm film was behaving in a bulk-like fashion its thermal expansion as itcools down should be closer to that of bulk ZrB₂, but the opposite isobserved: whereas for bulk ZrB₂ there is a |Δa|/a=0.58% contractionbetween 900° C. and 20° C., the contraction is 0.40% for the 200 nm filmand 0.14% for the 400 nm film. An examination of the temperaturedependence of the coincidence misfit provides some insight into thebehavior of the thick film: at the growth temperature, the film isessentially relaxed, even at the expense of a larger coincidence misfitF than in the 200 nm sample. However, it appears that upon cooling thefilm takes up strain as a way to minimize the coincidence misfit.Eventually, at room temperature, the coincidence misfit has been reducedto the same value as in the 200 nm film.

The above observations cannot be explained in terms of a strain energyequilibration model that includes only the Si substrate and the ZrB₂film. Even if one were to assume that additional misfit dislocationsrelax the growth-temperature strain in the 400 nm film, such anassumption would not lead to a simple explanation of the temperaturedependence of its lattice parameters. It appears that an explanationshould allow for the possibility that a thin interfacial layer with itsown elastic properties and strain status plays a role in the energyminimization.

The initial nucleation of ZrB₂ on Si(111) involves a √3×√3 Si surfacereconstruction with B atoms in a sub-surface layer and growth proceedsthrough the “6/5” coincidence mechanism (“magic” mismatch, supra). Theatomic structure of the interfacial layer is different from crystallineSi and ZrB₂, and cannot be modeled with bulk material properties. Thedifferent behaviors of the 200 nm and 400 nm films, as well as theobservation that all films have the same room temperature strain,regardless of thickness, are likely to require an interfacial layer withstrongly anharmonic elastic properties in which the elastic constantsare temperature-dependent, and perhaps even vary non-linearly.

Experimentally, the atomic positions in the nanometer-size interfacialregion cannot be determined from our HR-XRD measurements. However,significant strain fields running into the silicon were clearly visiblein HR XTEM micrographs obtained from these samples. In fact, a commonproblem encountered in the preparation of thin specimens for crosssectional TEM examination, was delamination of the thick film from thesubstrate, which was presumably caused by the large strains in thesilicon within the interface region.

Without being limited any one theory of operation, a schematicillustration of the strain distributions in the thin and thick ZrB₂films at the 900° C. growth temperature, including the interfaciallayer, is shown in FIG. 7. In the case of the thick, relaxed film, theZrB₂ applies a larger compressive stress on the interfacial layer, asshown by the “fade to black” contrast at the ZrB₂—Si interface in theright panel. The minimization of this stress may be the reason for thelarger than expected room temperature strain in the thick film, asindicated above. From a microstructural perspective the strain mismatchis accommodated by a fixed number of edge dislocations at the interface,consistent with the ˜6/5 coincidence, which “pin” the epilayer to thesubstrate to partially relieve the large misfit strain between the twomaterials. Thus the strains in ZrB₂ are determined by the thininitiation layer in the early stages of film growth (at 900° C.), andthis layer then serves as a robust template for subsequent film growth.Because of the high mechanical stiffness of the ZrB₂ lattice, theregistry adopted by this initial layer subsequently determines thestrain state of the rest of the ZrB₂ film at the growth temperature. Inthis study, it has been shown that this strain depends on thickness, andthat once a zero strain state is obtained there is in principle no upperlimit to the thickness that can be achieved on Si.

The thermal strain behavior observed in ZrB₂ films has significantimplications for the use of these materials as buffer layers for nitrideintegration with Si. The temperature dependence of the mismatch strainsbetween GaN and typical candidate substrates, including sapphire, SiCand bulk ZrB₂ are compared with ZrB₂/Si(111) in the inset of FIG. 8. Asshown here both sapphire and SiC exhibit constant mismatch strain overthe entire temperature range due to the large difference in latticeparameters between these substrates and GaN. For bulk ZrB₂ however, asystematic and significant decrease in mismatch strain is observed withincreasing temperature. This indicates that although there is betterlattice matching between bulk ZrB₂ and GaN relative to SiC and Al₂O₃,the nearly 10-fold thermal variation of mismatched strain in the formercould lead to cracking or other structural degradation in devices. Bycontrast the hybrid substrate based on 200 nm thick ZrB₂ film grown onSi(111) possesses the smallest mismatch strain, which vanishes at ˜400°C. and actually becomes negative at high temperatures (see main panel ofFIG. 8).

To our knowledge, this system represents the first “zero mismatch”template for GaN integration, exhibiting the smallest absolute value ofstrain over the entire temperature among the substrates considered. Forthe 400 nm thick film the strain is also very small relative to theother candidate substrates and exhibits essentially no temperaturedependence (see FIG. 8), indicating that this GaN/ZrB₂/Si(111)heterostructure based on thick ZrB₂ templates would experience thesmallest degree of thermal stress. Overall, these data demonstrate thesuperiority of our buffer approach for practical integration of nitrideswith silicon on both structural and thermoelastic grounds.

Example 4 Optical Properties of ZrB₂ Layers

A more detailed account of both the measurement and theoreticalsimulation of the ZrB₂ dielectric function ε(ω) and its reflectivityR(ω) in the energy range from ˜0.2-7 eV was investigated to identify theorigin of various characteristic spectral features in the reflectivityplot from the 1-7 eV range, and elucidate the low-energy (<1 eV)infrared properties, which are related to ZrB₂ metallic behavior.

Example 4a Electronic Structure Calculations of ZrB₂ Layers

State-of-the-art density functional theory calculations of theelectronic structure were carried out using the full-potentiallinearized augmented plane wave method (FPLAPW), as implemented in theEXCITING code. The Perdew-Zunger parameterization of theexchange-correlation potential and energy density of the Ceperley-Alderelectron gas functional were employed. (Perdew and Zunger, Phys. Rev. B23, 5048 (1981); Ceperley and Alder, Phys. Rev. Lett. 45, 566 (1980)) Atroom temperature ZrB₂ crystallizes in the AlB₂-type structure (spacegroup P6/mmm) with lattice constants a=3.186 Å and c=3.521 Å, and atomicpositions (in lattice coordinates) Zr: (000), B: (⅓⅔½), (⅔⅓½). Staticlattice optimization of the cell parameters at the LDA level using theFPLAPW method corroborates this equilibrium structure but yieldsslightly contracted lattice constants (a=3.145 Å, c=3.487 Å)corresponding to an underestimate of 3.5% in the volume per formulaunit. Part of this discrepancy is associated with the neglect ofzero-point energy and vibrational entropy effects, which are beyond thescope of the present study. To ensure meaningful comparisons between themeasured and simulated optical properties, all of our simulation studieswere carried out at the room temperature experimental structure of ZrB₂.

Well-converged self-consistent ground state solutions of the Kohn-Shamequations were obtained in the FPLAPW basis using R_(MT) K_(MAX)=7(product of the atomic sphere radii and the interstitial plane-wavecutoff), a maximum G-vector (G_(MAX)) of 12.0 in the expansion of theinterstitial density and potential, and an angular momentum cut-off ofl_(MAX)=10 for the corresponding density and potential within the atomicspheres, whose radii were set to 2.0 and 1.45 a.u. for Zr and B,respectively. Brillouin zone integration was carried out using thetetrahedron method on a 12×12×12 Γ-centered grid, corresponding to 133k-points in the irreducible wedge.

The band structure of ZrB₂, and the corresponding total density ofstates (DOS) are shown in FIG. 9. The figure also contains a schematicof the unit cell structure, and a sketch of the Brillouin zone and highsymmetry path used to plot the band dispersion. Perhaps the mostdistinct feature of the electronic structure is the “pseudogap”, whichappears as a valley in the DOS around the position of the Fermi level(E_(F)). Besides conferring semi-metallic properties to ZrB₂ it has beensuggested that the relatively low DOS near E_(F) leads to weakelectron-phonon coupling in this binary compound. The species andangular momentum decompositions of the DOS (partial DOS) are shown inFIG. 10, which indicate that the valence band structure is of a mixedhybrid nature devolving primarily from an admixture of B p-states and Zrd-states. The lowest lying bands in this energy range are largely Borons-like, and account for the ˜4 eV wide feature near −10 eV. The DOS inthe conduction band is dominated by contributions from the Zr d-statesup to 10 eV above E_(F), while Boron p-states account for the featuresat higher energies as shown in the Figure.

All of the simulated optical properties described in the present workare obtained from the complex dielectric function ε(ω)=ε₁(ω)+i ε₂(ω). Inthe case of semi-metallic ZrB₂ both interband and intraband transitionscontribute to the dielectric response, with the latter dominating at lowenergies. Three particle interactions between electrons, photons andphonons can also in principle produce indirect interband and intrabandelectronic transitions. While the incorporation of these effects isbeyond the scope of the present work it is believed that theyessentially contribute a smooth background to the spectral response(Smith, Phys. Rev. B, 3 1862 (1971)). In this work, only directinterband and intraband transitions were explicitly included. Theinterband component of the imaginary part ε₂(ω)) of the dielectricfunction is obtained within the random phase approximation (RPA) as

$\begin{matrix}{{ɛ_{2}(\omega)} = {\frac{\hslash^{2}e^{2}}{\pi \; m^{2}\omega^{2}}{\sum\limits_{n,m}{\int{{k}{{p_{n,m,k}}^{2}\left\lbrack {{f\left( E_{n,k} \right)} - {f\left( E_{m,k} \right)}} \right\rbrack}{\delta \left( {{E_{n}(k)} - {E_{m}(k)} - {\hslash\omega}} \right)}}}}}} & \lbrack 1\rbrack\end{matrix}$

where p_(n,m,k) are the momentum matrix element for the transition frombands n and m at wave-vector k, with corresponding band energiesE_(n)(k) and E_(m)(k), and f(E) are occupation numbers. The real partε₁(ω) is then obtained from a Kramers-Kronig integration:

$\begin{matrix}{{ɛ_{1}(\omega)} = {1 + {\frac{2}{\pi}P{\int_{0}^{\infty}{{\omega^{\prime}}{\frac{\omega^{\prime}{ɛ_{2}\left( \omega^{\prime} \right)}}{\left( {\omega^{\prime 2} - \omega^{2}} \right)}.}}}}}} & \lbrack 2\rbrack\end{matrix}$

To model the contribution from direct intraband transition, the Drudeexpression ε^(Drude)(ω)=1−ω_(p) ²/(ω²+iωΓ), where Γ is the lifetimebroadening (Γ˜0.11 eV, corresponds to a relaxation time of ˜7 fs, seebelow) and ω_(p) is the free-electron plasma frequency, given by theexpression:

$\begin{matrix}{\omega_{p}^{2} = {\frac{\hslash^{2}e^{2}}{\pi \mspace{11mu} m^{2}}{\sum\limits_{n}{\int{{k}{p_{n,n,k}}^{2}{{\delta \left( {E_{n,k} - E_{F}} \right)}.}}}}}} & \lbrack 3\rbrack\end{matrix}$

were adopted. For binary crystals with hexagonal symmetry, like ZrB₂,the optical response is in general anisotropic with two independentcomponents for ε(ω) and ω_(p) corresponding to electric fieldpolarizations E ∥ c and E ⊥ c. These are obtained by evaluating thematrix elements appearing in Eq. 1-3 using appropriate momentum operatorcomponents.

It should be noted that a very dense 40×40×40 k-point mesh (3234irreducible k-points) was required to converge the linear opticalproperties, including the plasma frequency. The number of empty statesin the optics calculations was increased to capture higher energytransitions that may be involved in the optical spectrum. Using thelatter grid ω_(p) ^(xx)=4.29 eV and ω_(p) ^(zz)=4.06 eV were obtainedfor the plasma frequencies in basal plane and parallel to the c-axis,and an isotropic average value of 4.21 eV. This is smaller than anearlier reported value 4.56 eV obtained using a coarser grid of 2130k-points. Once convergence was achieved, the normal incidentreflectivity for both polarizations was calculated from the dielectricfunctions defined above using the Fresnel equation

$\begin{matrix}{R = \frac{\left( {n - 1} \right)^{2} + k^{2}}{\left( {n + 1} \right)^{2} + k^{2}}} & \lbrack 4\rbrack\end{matrix}$

where n and k are the real and imaginary part of the complex refractiveindex defined by n+ik=√{square root over (ε)}. The isotropic values ofthe dielectric functions, plasma frequencies and reflectivities (seebelow) were obtained taking an average according to

${{\langle N\rangle} = {\frac{1}{3}\left( {{2N_{a}} + N_{c}} \right)}},$

where N_(a) and N_(c) are quantities corresponding to the basal planeand c-axis, respectively.

Example 4b

Optical Properties from Ellipsometry of ZrB₂ Layers

Spectroscopic ellipsometry measurements were carried out at roomtemperature using a Variable-Angle Spectroscopic Ellipsometer with acomputer-controlled compensator, and an Infrared Variable AngleSpectroscopic Ellipsometer (IR-VASE) with a rotating compensator (see,Herzinger et al., J. Appl. Phys. 83 (6), 3323-3336 (1998)). This systemis based on a Fourier-Transform Infrared Spectrometer. Both instrumentsare manufactured by J.A. Woollam Co. We studied in detail two ZrB₂samples with different thickness (˜50 nm and 150 nm). Using thevisible-UV instrument, the dielectric function of the films wasdetermined from 0.74 eV to 6.6 eV with 0.03 eV steps. Two angles ofincidence (70° and 80°) were used. Infrared measurements at an angle ofincidence of 60° were carried out for the 150 nm sample. Thesemeasurements covered the 0.03 eV to 0.83 eV range.

The ZrB₂ films were modeled as a three-layer system consisting of a Sisubstrate, a film layer and a surface layer. Since ZrB₂ is opticallyabsorbing, there is a strong correlation between thickness of the filmand optical constants (McGahan, et al. Thin Solid Films 234 (1-2), 443(1993)). In order to extract reliable optical data, the surface layerwas modeled as a thin film consisting of 50% ZrB₂ and 50% voids in theBruggeman approximation (see, Craig F. Bohren and Donald R. Huffman,Absorption and Scattering of Light by Small Particles. (WileyInterscience, New York, 1983), p. 530). The thicknesses of the surfacefilms were taken as twice the surface roughness RMS value, as obtainedfrom the AFM measurements, and were kept fixed in the fitting process.The thicknesses of the ZrB₂ films were taken as equal to the thicknessdetermined from the RBS measurements minus the AFM roughness RMS value,and they were also kept fixed. Finally, the optical constants for the Sisubstrate were taken from the literature (Herzinger, et al, J. Appl.Phys. 83 (6), 3323-3336 (1998)). These assumptions fix all parameters ofthe optical model except for the optical constants of ZrB₂, which arethen obtained from a point-by-point fit (see, Perucchi, et al. Phys.Rev. Lett. 92 (6), 067401 (2004)).

The model assumes an isotropic dielectric function tensor, which is notrequired by symmetry in ZrB₂ but is justified as a good approximation bythe theoretical simulations described above which predict that theanisotropy in the reflectivity is essentially zero over most of theenergy range considered, with a maximum deviation of <10% . Theself-consistency of the fit was verified by keeping the point-by-pointoptical constants fixed, while allowing the thicknesses of the two toplayers (diboride and surface) to vary. The fit converged to the samevalues of thicknesses for surface layer and film layer that were assumedbased on the AFM and RBS data. The optical constants obtained from thetwo samples were virtually the same. Since the films thicknesses arevery different, this lends further support to the reliability of thefits. The maximum deviation between the two samples for the real part ofthe refraction index is Δn=0.2 in the UV while for the imaginary part,the deviation is Δk<0.1. The reflectivity of the two samples obtainedusing the above procedure was virtually identical. Finally, theKramers-Kronig consistency of the optical constants was confirmed byverifying that the point-by-point fit dielectric function can beaccurately described with an optical dispersion model consisting ofGaussian oscillators.

The real and imaginary parts of the complex dielectric function in theinfrared are shown in FIG. 11. As can be seen from this figure, thedielectric function displays the typical metallic Drude behavior in theinfrared. The data is fit with an expression of the form

ε(ω)=1+ε^(Drude)(ω)+ε^(inter)(ω).   [5]

Here ε^(inter)(ω) corresponds to interband transitions, which aremodeled as Gaussian oscillators, and the Drude term is given in terms ofthe plasma frequency ω_(p) and the relaxation time τ (or, alternatively,in terms of the DC resistivity ρ_(dc) and τ) as

$\begin{matrix}{{ɛ^{Drude}(\omega)} = {{- \frac{\omega_{p}^{2}}{\omega^{2} + {{\omega}/\tau}}} = {- {\frac{4\pi}{\rho_{d\; c}\left( {{\omega^{2}\tau} + {\omega}} \right)}.}}}} & \lbrack 6\rbrack\end{matrix}$

The plasma frequency can be expressed as ω_(p) ²=4πne²/m_(opt), where nis the conduction electron density and m_(opt) is the average opticalmass. The fit parameters are ω_(p)=4.22 eV and τ=9.0 fs. The value ofthe plasma energy is in excellent agreement with the FPLAPW-LDAprediction of 4.21 eV. From these parameters we find ρ_(dc)=30.6 μΩcm.Transport measurements in single ZrB₂ crystals yield a room temperatureresistivity ρ_(dc) (300 K)=6-10 μΩcm, which implies τ˜30-45 fs, and aresidual low-temperature resistivity ρ₀=0.5-2 μΩcm (see, Gasparov, etal., Phys. Rev. B 73 (9), 094510 (2006,); Forzani et al., EuropeanPhysical Journal B 51 (1), 29 (2006)). A comparative analysis of thefilm and bulk results in the spirit of Matthiesen's rule suggests forour film samples a residual low temperature resistivity ρ₀=21-25 μΩcm,about one order of magnitude higher than in bulk single crystals. Weemphasize, however, that we are comparing optical data from films withtransport measurements in bulk crystals. Discrepancies have been notedbetween transport and optical measurements of the DC resistivity insystems with an optical response characterized by more than one Drudeterm. The ZrB₂ material could be such an example, since it has a complexconduction band structure with several charge pockets at the Fermilevel.

The is fit very well with a single Drude term, the parameters of theDrude expression in Eq. 6 remain stable if the fit is limited to a verynarrow low-frequency range), but the presence of an additional Drudeterm that might become apparent at extremely low frequencies (beyond thereach of our ellipsometer) cannot be ruled out. Ellipsometricmeasurements on bulk ZrB₂ single crystals should shed light on possiblediscrepancies between transport and optical data in this system.

If it is assumed that the optically derived resistivity can be comparedwith transport data, the higher resistivity of our material may resultfrom its thin film nature. In fact, a similar effect is observed in theiso-structural MgB₂ compound, for which the residual resistivity in 400nm-thick films grown on sapphire substrates is five times larger than insingle crystal MgB₂ (see, Kim, et al., Phys. Rev. Lett. 87 (8), 087002(2001); Masui, et el., Phys. Rev. B 65 (21), 214513 (2002).

The residual resistivity in bulk ZrB₂ crystals is very low compared toMgB₂, which magnifies the relative contribution of possible filmdefects. The only defects that we have observed in our ZrB₂ films arethe strain relieving edge dislocations located at the interface.Threading analogs typically observed in mismatched heteroepitaxy are notpresent in our case. On the other hand, interface roughness scatteringis known to make a significant contribution whenever the film thicknessd is much less than the carrier mean free path l. (Guy Fishman andDaniel Calecki, Phys. Rev. Lett. 62 (11), 1302 (1989)).

Using de Haas-van Alphen data for ZrB₂ (see, Forzani, et al. EuropeanPhysical Journal B 51 (1), 29 (2006)), a Fermi velocity v_(F)=1.2×10⁸cm/s was estimated which at room temperature leads to l˜50 nm in thebulk material. Thus roughness scattering at the Si/ZrB₂ interface is notexpected to be the main reason for the increased resistivity in ourd=150 nm film. Similarly, the XRD discussion above suggests grain sizesof at least 500 nm, so that grain boundary scattering is not likely toplay a dominant role.

The real and imaginary parts of the dielectric function from the near-IRto the UV are shown in FIG. 12, and the correspondent air reflectivity(including the Drude region) is shown in FIG. 13. As mentioned above,the available optical data for ZrB₂ was the work of Oda and Fukuicovering the 1.4-25 eV energy range, which is also plotted in FIG. 13and compared with the instant data. A reasonable agreement is seen inthe region below 3 eV, but at higher energies there is a rather abruptdrop in reflectivity in Oda and Fukui's data that is found neither inour experimental or simulated data (FIG. 13 solid and dotted line,respectively). On the other hand, both data sets agree well on theenergy of the three features at 2.6 eV, 4.3 eV, and 5.7 eV, which arerelated to interband transitions.

The values of the visible/UV reflectivity shown here are slightly higherthan those previously reported. The reason for the discrepancy may arisefrom that the thicknesses of the surface layer and the ZrB₂ film wereallowed to vary in the fitting process, whereas here the RBS and AFMvalues have been chosen, as discussed above. The latter approachproduces more consistent results when a common model is sought to fitellipsometric measurements of ZrB₂ and Hf_(x)Zr_(1−x)B₂ alloys. Thediscrepancy between the two fitting procedures for ZrB₂ provides anestimate of the error in the ellipsometric determination of thedielectric function. However, neither the infrared reflectivity nor theenergy of the visible/UV interband features are affected by the choiceof fitting procedure.

FIG. 13 also compares the observed reflectivity with our LDAsimulations. The dotted line represents the isotropic averagereflectivity, while the inset is a plot of the anisotropy calculated asthe difference between the reflectivity corresponding to an E-fieldperpendicular and parallel to the ZrB₂ c-axis, respectively. Simulationspredict that the reflectivity is essentially isotropic (R_(⊥)-R_(∥)˜0)over most of the energy range from 0-10 eV, but that significantdeviations on the order of 5-10% are expected near 4.4 and 9.5 eV. Ascan be seen from the comparison the theoretical reflectivity reproducesthe experimental data fairly well, including the positions of the mainexperimental spectral features labeled A (2.6 eV), B (4.3 eV) and C (5.7eV) in the figure. The corresponding values from simulation are 2.2, 4.4and 5.5-5.7 eV, respectively. For energies <1 eV the simulated resultsslightly underestimated the observed reflectivity using a calculatedvalue of

ω_(p)=4.21 eV and a best fit value of

=7 fs. The slightly lower value for the lifetime obtained here is likelyassociated with the differences between the calculated and measuredinterband component to the reflectivity, which is non-empirical in theformer case. The agreement between theory and experiment in the lowenergy range indicates that the single oscillator assumption used in theexperimental fitting is a good approximation.

To fully elucidate the origin of the observed spectral features labeledA, B and C in FIG. 13 a detailed analysis of the electronic bandstructure was carried out. By systematically sorting the momentum matrixelements corresponding to interband transitions (see Eq.1) according toboth energy and k-point index band combinations were identified withdominant spectral weight for each of the three features. According tosimulations these transitions do not occur at high-symmetry points inreciprocal space, but rather from narrow regions within the Brillouinzone as described by the segments below each panel corresponding to eachfeature in FIG. 14. Here the values of the parameters κ_(A), κ_(B) andκ_(C) are given in terms of lattice coordinates in k-space:

${k_{1} = {\frac{2\pi}{\left( \frac{a\sqrt{3}}{2} \right)}\left( {1,0,0} \right)}},{k_{2} = {{\frac{2\pi}{\left( \frac{a\sqrt{3}}{2} \right)}\left( {{1/2},\frac{\sqrt{3}}{2},0} \right)\mspace{14mu} {and}\mspace{14mu} k_{3}} = {\frac{2\pi}{c}{\left( {0,0,1} \right).}}}}$

From these plots it is evident that features A and B at 2.2 eV and 4.4eV, respectively, involve transitions from band 9 to band 10 whilefeature C in the vicinity of 5.5-5.7 eV involves direct interbandtransitions from band 8 to band 11 (see numbering in the band structureof first panel, FIG. 14). The grey areas shown in FIG. 14 denote theapproximate range corresponding to the largest momentum matrix elements.

Example 5 ZrHfB₂ Alloys

High-quality heteroepitaxial Hf_(x)Zr_(1−x)B₂ (0≦x≦1) buffer layers havebeen epitaxially grown directly on Si(111). The compositional dependenceof the film structure, and ab initio elastic constants, show thathexagonal Hf_(x)Zr_(1−x)B₂ alloy layers possess tensile in-plane strain(approximately 0.5%) as grown

Si(111) substrates were outgassed in the MBE chamber at 650° C. and thenative oxide was removed by flashing at 1200° C. The Hf(BH₄)₄ andZr(BH₄)₄ gasses were then allow to react on the substrate surface at900° C. and 1-20×10⁻⁶ Torr (base pressure 10⁻¹⁰ Torr) for approximately30-120 minutes, depending on film thickness. Under these conditions bothprecursors thermally decomposed to form films according to:

(1−x)Zr(BH₄)₄ +xHf(BH₄)₄→Zr_(1−x)Hf_(x)B₂+B₂H₆+5 H₂

The relationship can be further generalized to include Aluminum andcorresponding expressions that relate the precursors to the formation offilms of Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1, 0≦y≦1) and can be writtenaccordingly. For example, the generated diborane as byproducts or BH₄ ⁺moieties, can react with atomic Al to produce solid AlB₂.

FIG. 15( a) shows an RBS spectrum of a Zr_(0.70)Hf_(0.30)B₂ sample witha nominal thickness of 50 nm. The ratio of the aligned vs. the randompeak heights (χ_(min)) is 6% for both Hf and Zr, indicating their fullsubstitutionality in the alloy and the high degree of epitaxialalignment of the film with respect to the Si substrate. XTEM indicatesthat the layers are perfectly monocrystalline, highly coherent andatomically flat (FIG. 15 b and FIG. 15 c).

The lattice misfit is taken up by pure edge-type dislocations viainsertion of extra {1100} planes along the [1120] direction. Diffractioncontrast micrographs reveal that no threading dislocation corespropagate to the surface within the field of view of approximately 3 μm.Electron energy loss spectroscopy (EELS) with a nanometer-sized electronprobe shows that the constituent Zr and Hf elements appear together atevery nanometer scale region probed without any segregation of theindividual alloy components. Atomic force microscopy (AFM) revealed asmooth surface with a roughness of approximately 2 nm for a 5×5 μm² areawhich is highly suitable for buffer layer applications. The surfacemorphology further improves by ex situ annealing of the films at 900° C.and 10⁻⁹ Torr for 8 hours. This yields a roughness below 1.5 nm and asurface consisting of large atomically flat areas connected by steps.

For all Zr_(1−x)Hf_(x)B₂ films that have been characterized, HR-XRDon-axis scans show the (001) and (002) peaks of the AlB₂ structure,oriented with (0001) parallel to the Si(111). The ZrHfAlB₂ family ofdiborides has a layered structure which is referred to generally as “theAlB₂” structure. The (002) peaks, which are more sensitive to thecompositional changes of the alloys, were significantly shifted fromthose of pure ZrB₂. The absence of splitting or broadening in thesepeaks corroborates the full substitutionality of both Hf and Zr atoms inthe lattice. Thickness fringes were observed in the vicinity of the(001) and (002) reflections, confirming the high quality of theinterface and the uniformity and smoothness of the layers. Accurate aand c lattice parameters were extracted from the asymmetric (−113)reciprocal space maps of the AlB₂ structure and are provided in Table 1for samples with thicknesses of ˜50±5 nm. Due to strain, these measuredlattice parameters do not correspond to the relaxed hexagonal latticeparameters a₀ and c₀.

For hexagonal films with the [0001] plane oriented normal to thesubstrate, the perpendicular (ε_(c)) and parallel (ε_(a)) strains aregiven by ε_(c)=−2C₁₃ε_(a)/C₃₃ where εc=(c-c₀)/c₀ and ε_(a)=(a-a₀)/a₀.C₁₃ and C₃₃ are elastic tensors. For bulk ZrB₂ and HfB₂ the known c/aratios (denoted by η below) are slightly different (1.114 and 1.108,respectively). Therefore, in order to determine the strain state thefollowing approximations were made: (i) η for the relaxed epitaxial filmis identical to that of the equilibrium bulk crystals and (ii) the c/aratio (η) and elastic ratio ξ=−2C₁₃/C₃₃ are both linear functions ofcomposition; η(x)=xηHfB₂+(1−x)ηZrB₂ and ξ(x)=xξHfB₂+(1−x)ξZrB₂,respectively. Since the elastic constants of both ZrB₂ and HfB₂ aregenerally not well known, the Vienna ab initio simulation package (VASP)DFT code (which is described by G. Kresse and J. Furthmüller in Phys.Rev. B 54, 11169 (1996), and G. Kresse and J. Furthmüller, in Comput.Mater. Sci. 6, 15 (1996), both of which are incorporated herein byreference) was used to calculate them using finite strain deformationsof the equilibrated systems. Additional information about the theory ofthe elastic constants of hexagonal transition metal materials was givenby Fast et al., in Phys. Rev. B 41, 17431 (1995), incorporated herein byreference. From inversion of the strain relation the relaxed latticeconstants are then given by a₀(x)={c(x)η(x)−ξ(x)a(x)}/{1−ξ(x)} andc₀(x)=η(x)·a₀(x), and these are listed in Table 4 (infra). The relaxedfilm lattice constant of the end members match the known values for thebulk phases. This provides additional justification for theapproximations discussed above.

The relaxed lattice constants for the alloys follow Vegard's law quiteclosely. Our analysis shows that ZrB₂ and the alloy films exhibit aslight tensile strain (ε_(a)˜+0.50%, ε_(c)˜−0.29%), while the HfB₂ filmis strained even more (ε_(a)˜+0.66%, ε_(c)˜−0.36%). The fact that all ofthe films (including ZrB₂) were found to be tensile strained hassignificant implications for lattice engineering, since this providesbetter matching with Ga-rich alloys. In particular, the measured valueof a for the ZrB₂ films is essentially identical to that of GaN.

FIG. 16( a) shows Rutherford backscattering (RBS) spectra obtained for a45 nm thick Hf_(0.5)Zr_(0.5)B₂ alloy grown on 85 nm thick ZrB₂ bufferlayer. Both Zr and Hf show a high degree of alignment (low trace) whichis consistent with high crystallinity and perfect epitaxial registry.FIG. 16( b) shows high resolution X-ray reciprocal space maps of the(−113) peaks of the Hf_(0.5)Zr_(0.5)B₂ and ZrB₂ buffer layer showing theprecise lattice constant values within the heterostructure.

Example 6

Epitaxial Zr_(x)Hf_(y)Al_(1−x−y)B₂ Layers

Exemplary films of Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1, 0≦y≦1) have beengrown according to the methods of the preceding examples by theinclusion of an atomic Al source, and characterized by Rutherfordbackscattering (RBS), high resolution cross sectional transmissionelectron microscopy (XTEM), Z-contrast imaging, and high resolutionx-ray diffraction (HR-XRD). These tunable structural, thermoelastic andoptical properties suggest that Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1, 0≦y≦1)templates are suitable for broad integration of III nitrides with Si. Asan example of embodiments, Zr_(x)Hf_(y)Al_(1−x−y)B₂ (0≦x≦1, 0≦y≦1) filmshave been grown with y=0 (i.e. alloys of Zirconium and Hafnium).

Example 7 HfB₂/ZrB₂/Si(111)

High quality HfB₂ films were also grown on strain compensatingZrB₂-buffered Si(111). Initial reflectivity measurements of thick ZrB₂films agree with first principles calculations which predict that thereflectivity of HfB₂ increases by 20% relative to ZrB₂ in theapproximately 2-8 electron volt (eV) energy range. Wavelength (λ)(measured in micrometers (μm) is reciprocally related with energy(measured in eV) through the relationship

λ(μm)=1.24/Energy (eV)

As noted above, the in-plane strain systematically increases in theHf-rich compositional regime with a concomitant reduction in growth rate(approximately 0.5 nm/min, for pure HfB₂). The increase in strainreduces the reactivity and surface mobility. In fact, for HfB₂ thegrowth on Si(111) eventually produces almost exclusively rough filmswith large surface undulations (AFM roughness, >15 nm). The growth, inthis case, was conducted at 900° C. via decomposition of pure Hf(BH₄)₄under conditions similar to those described above for the alloys. TheRBS and XTEM data confirmed the presence of predominately rough layersdominated by ensembles of large islands. Nevertheless, and in spite ofthe slightly larger film strain (see Table 4), the data also showedstoichiometric and aligned materials with sharp and commensurateinterfaces. XRD off axis measurements gave a=3.160 Å and c=3.467 Å whichare larger/smaller than a=3.142 Å, c=3.48 Å of bulk HfB₂, due to strainimposed by the Si substrate.

Further, growth of HfB₂ films on isostructural ZrB₂ buffers (rather thanon directly on the Si(111) surface) to promote formation of smooth filmssuitable for nitride integration were pursued. These HfB₂ films growmuch more readily (˜2 nm/min.), and exhibit exceptional morphologicaland structural properties, including flat surfaces (AFM roughness 2 nm),highly coherent interfaces and virtually defect free microstructures.The XRD measurements show that the layers are partially strained and thelattice parameters are close to those of HfB₂ films grown on Si(Table4).

TABLE 4 Lattice parameters of Zr_(1−x)Hf_(x)B₂ films obtained fromHR-XRD analysis (bold font). The relaxed lattice parameters (a₀ and c₀)and calculated strains (ε_(a) and ε_(c)) are obtained from acompositional interpolation of the elastic ratio ξ(x) and bulk c/a ratioη(x). X 0 0.15 0.3 0.6 1 A 3.187 3.183 3.176 3.167 3.160 ε_(a) +0.52+0.54 +0.50 +0.48 +0.66 C 3.521 3.513 3.505 3.491 3.467 ε_(c) −0.30−0.32 −0.28 −0.27 −0.36 ξ(x) −0.584 −0.580 −0.574 −0.565 −0.552 η(x)1.114 1.113 1.112 1.111 1.108 a₀ 3.170 3.166 3.160 3.152 3.140 c₀ 3.5313.524 3.515 3.501 3.480

Growth of thin HfB₂ layers on oxidized Si via decomposition of Hf(BH₄)₄,has been reported by Jayaraman et al., in Surf Coat. Tech. 200(22-23),6629 (2006), incorporated herein by reference, but no evidence ofepitaxy was given. The XTEM data indicates that the ZrB₂ buffers bridgethe strain differential between HfB₂ and Si, allowing formation ofperfectly epitaxial HfB₂ films that cannot be obtained directly on Si.Thus a subsequent ZrHfAlB₂ diboride film can be epitaxially deposited ona ZrB₂ layer that is epitaxially deposited on the substrate to promotegrowth of the subsequent diboride film. XTEM Z-contrast images and EELSprofiles of Zr and Hf across the interface showed an abrupt transitionof the elements from ZrB₂ to HfB₂ with no evidence of intermixingbetween the two materials at the nanometer scale (FIG. 17).

Example 8

Zr_(1−x)Hf_(x)B₂/ZrB₂/Si(111)

The Zr_(1−x)Hf_(x)B₂ alloys with compositions across the entirehomogeneity range were produced via reactions of the Hf(BH₄)₄ andZr(BH₄)₄ precursors by gas source MBE. The growth was performed usingprocedures similar to those described above. Briefly, the freshlyprepared Hf(BH₄)₄ and Zr(BH₄)₄ gaseous precursors were diluted withresearch grade H₂ at 2% by volume and stock mixtures were produced bymixing at the desired molar ratios which were found to determine thefinal composition of the alloy. Prior to each deposition, the mixtureswere checked by gas IR which confirmed that the individual componentsdid not react or decomposed even when kept for extended time periods.The Si(111) substrates were sonicated in methanol to remove organicimpurities from the surface, and then loaded into the MBE chamber. Theywere outgassed at 650° C. until the pressure was restored to the basevalue (10⁻⁹ Torr), and then flashed at 1200° C. to desorb the nativeoxide. The reactions were conducted at an temperature of 900° C. and atpressures ranging form 1×10⁻⁶ to 2×10⁻⁵ Torr for 2-5 hours depending onthe target film composition and thickness.

The compositional and morphological properties of the samples werecharacterized using the same techniques as detailed above for theHfB₂/ZrB₂/Si(111) system, and the data in general indicated materialswith similar quality. Here we focus on the strain behavior of selectedHf_(x)Zr_(1−x)B₂/ZrB₂/Si(111) andHf_(y)Zr_(1−y)B₂/Hf_(x)Zr_(1−x)B₂/Si(111) samples (with y>x) obtainedvia measurements of the (113) reciprocals space maps. A typical exampleinvolves a Hf_(x)Zr_(1−x)B₂/ZrB₂/Si(111) sample consisting of an ˜300 nmthick Hf_(0.25)Zr_(0.75)B₂ alloy grown on a 35 nm thick ZrB₂ buffer. Thein-plane lattice constant of the buffer (3.1699 Å) is smaller than that(3.189 Å) observed in the as grown ZrB₂/Si(111) sample with the samethickness implying that the Hf_(0.25)Zr_(0.75)B₂ overlayer has induced acompression in the underlying ZrB₂ template. The lattice constant of theHf_(0.25)Zr_(0.75)B₂ (3.1692 Å) is significantly larger than its relaxedalloy value (3.160 Å) indicating that the overlayer is tensile strained.Overall these results show the general behavior that the epilayercompresses the much thinner buffer which in turn induces a tensile trainon the epilayer. Consequently the entire Hf_(0.25)Zr_(0.75)B₂/ZrB₂ filmis fully coherent and tensile strained with respect to the substrate.

The strain properties of this sample were compared to a relatedHf_(0.5)Zr_(0.5)B₂/ZrB2/Si(111) heterostructure in which the overlayerhas a significantly higher Hf content and is also much thinner than thebuffer (45 and 80 nm, respectively). The measured in-plane latticeconstants are 3.183 Å and 3.186 Å, respectively, indicating that the twolayers are essentially lattice matched.

In contrast to the previous sample, the epilayer in this case exhibits alarger lattice constant in spite of its higher Hf content while that ofthe buffer is essentially unchanged (a=3.189 Å) compared to its originalstrain state. This observation indicates that the thicker buffer imposesa significant tensile strain on the overlayer and the entire stack istensile strained to the substrate. In both examples described here thestrain state of the combined boride layers is intimately dependent onthe thickness and composition of the individual layers, as expected.

Example 9 Optical Properties of HfB₂/ZrB₂/Si

Spectroscopic ellipsometry measurements were carried out on aHfB₂/ZrB₂/Si sample prepared according to the preceding examples with aHfB₂ thickness of ˜70 nm and a ZrB₂ thickness of ˜70 nm as measured byRBS. The dielectric function was measured from 0.74 eV to 6.6 eV with0.02 eV steps using three angles of incidence: 65°, 70° and 75°.Measurements between 0.03 eV to 0.83 eV were performed with the infraredellipsometer using three angles of incidence: 60°, 65° and 75°. TheHfB₂/ZrB₂/Si stack was modeled as a five-layer system consisting of a Sisubstrate, a ZrB₂ buffer layer, an interface roughness layer, a filmlayer and a surface layer. As in the ZrB₂ case, the surface layer wasmodeled as a thin film consisting of 50% HfB₂ and 50% voids in theBruggeman approximation. The thicknesses of the surface films were takenas twice the surface roughness rms value, as obtained from the AFMmeasurements, and were kept fixed in the fitting process. The thicknessof the HfB₂ layer was taken as equal to the thickness determined fromthe RBS measurements minus the AFM roughness rms value. For the bufferlayer we used the optical constants of ZrB₂ described in a previouspublications. The optical constants of HfB₂, which were then obtainedfrom a point-by point-fit. An isotropic dielectric function tensor wasassumed.

Additionally, a sample with an additional ZrB₂ cap layer as well as HfB₂layers grown on Hf_(x)Zr_(1−x)B₂ buffer layers was studied. Whereas theinfrared data from these samples agrees within experimental error, thevisible/UV HfB₂ dielectric function appears sample-dependent. We showinfrared results in FIG. 18 and visible-UV data for aHfB₂/Hf_(x)Zr_(1−x)B₂/Si(111) sample in FIG. 19. The correspondingreflectivities are compared with those of ZrB₂ in FIG. 20. The finestructure between 2 eV and 6 eV appears consistently at the sameenergies in all HfB₂ samples, in spite of the somewhat differentabsolute values of the reflectivity and that these energies are shiftedrelative to ZrB₂. This is consistent with an explanation in terms ofinterband transitions. Results from a series of Hf_(x)Zr_(1−x)B₂ alloysamples, to be presented elsewhere, show that the energies have a smoothcompositional dependence between ZrB₂ and HfB₂.

Analysis of the infrared dielectric function of HfB₂ was similar to theZrB₂ study discussed above. The fit of the data includes a Drude termand the fit parameters are hω_(p)=4.27 eV and τ=7.5 fs. From theseparameters we find ρ_(dc)=35.6 μΩcm. The reported room temperatureresistivity in bulk HfB₂ is ρ_(dc) (298 K)=8.8 μΩcm, so that the resultswere very similar to those obtained from ZrB₂ films.

Example 10 Growth on Miscut Si(111) Wafers

While the buffer layer approach described in the preceding examplesprovides a systematic direct path to significant materials improvement,and yielded key structural and optical data for Hf-rich systems thatcannot otherwise be achieved, the presence of residual strains and theneed for multistep processing prompted a search for an alternative thatwould be practical for larger scale integrations schemes.

It has been unexpectedly found that Hf_(x)Zr_(1−x)B₂ films with superiormorphological quality can be grown directly on Si wafers that are miscutby ˜4 degrees (FIG. 21). This technique allows growth of thick filmswith a remarkably homogeneous surface roughness suitable forspectroscopic ellipsometry measurements of the dielectric functiondevoid of artifacts and ambiguities. This is a significant newdevelopment which has the potential to produce for the first time largeformat, Hf-rich hybrid substrates with optimal structural and opticalquality.

Example 11 Group III Nitride Growth on Epitaxial Layer GaN/ZrB₂/Si(111)

GaN has been epitaxially grown on buffer layers. The layers were grownby chemical vapor deposition (CVD), although other techniques forepitaxial growth of nitrides can also be used

In a typical experiment. a Si(111) substrate surface was cleaned byflashing briefly to 1150° C. and 4×10⁻¹⁰ Torr. Immediately thereafter athick ZrB₂(0001) buffer layer (100 nm) was grown at 900° C. viadecomposing of Zr(BH₄)₄. The subsequent growth of GaN was conducted byadmitting a single source H₂GaN₃ or D₂GaN₃ precursor via a nozzlepositioned 2 cm away from the substrate surface at a pressure 2×10⁻⁷Torr established by the vapor pressure of the compound at roomtemperature. Films with a nominal 500 nm thickness were produced at 550°C. and were found to display flat surfaces with RMS roughness of 2 nmand highly aligned microstructures devoid of threading defects withinthe field of view of the XTEM micrographs. The quality of the materialsproduced via this method is also reflected in their luminescentproperties, which are comparable to those of undoped GaN films grown onsapphire by MOCVD at ˜1050° C.

FIG. 22 shows a cross-sectional transmission electron microscopy (XTEM)image of a GaN/ZrB₂/Si(111) semiconductor structure according to theinvention. FIG.23 is a PL spectrum of a GaN/ZrB₂/Si(111) semiconductorstructure according to the invention. The CVD growth temperature was550° C., although it will be understood other growth temperatures canalso be used. The films exhibit intense photoluminescence (PL)indicative of band-edge emission for a single-phase hexagonal GaN. ThePL peak at 10 K is located at 359 nm with a FWHM of 15 nm, close to theneutral donor bound exciton D⁰X line at 3.47 eV usually associated withlow-temperature PL of GaN films. No yellow luminescence around 560° C.is found for both room temperature and low-temperature PL.

Example 12 Group III Nitride Growth on Epitaxial LayerAlGaN/GaN/ZrB₂/Si(111)

An AlGaN overlayer was applied to the structure of Example 11 to form anAlGaN/GaN/ZrB₂/Si(111) heterostructure via thermally activated reactionsof D₂GaN₃ vapors and elemental Al (99.999% pure) which was evaporatedfrom a Knudsen cell as shown in FIG. 24( a). The reactive flux of the Alatoms at the substrate surface (˜1-3 Å/min) was measured using a crystalthickness monitor. The D₂GaN₃ vapor was introduced into the chamberthrough a leak valve at a pressure range of 2-8×10⁻⁷ Torr. Under theseconditions and with the substrate temperature held at 700° C. perfectlyhomogeneous and monocrystalline alloy films were produced.

The growth rate of the AlGaN layer via this method was 4 nm per minuteto deposit transparent films with nominal thickness of 150 nm.Rutherford backscattering spectrometry (RBS) was used to determine theelemental composition, and estimate the film thickness. The resultsshowed that the Al content in the final product was systematically tunedwith in the ˜2-10% range by adjusting the flux ratio of the D₂GaN₃ andAl gaseous species in the reaction environment. The RBS determinedcompositions were corroborated by high resolution XRD measurements ofthe (002) and (004) reflections assuming perfect Vegard's Law behaviorin the Ga_(1−x)Al_(x)N system.

Photoemission from a 150 nm thick Al_(0.08)Ga_(0.92)N film was obtainedusing a cathodoluminescence (CL) spectrometer fitted to a scanningelectron microscope. FIG. 24 shows a typical CL spectrum exhibitingstrong band gap emission peaks with a wavelength maximum at 346 nm whichcorresponds to a composition of Al_(0.10)Ga_(0.90)N. The peak FWHM is 20nm is comparable to that of pure GaN grown on ZrB₂ via decomposition ofD₂GaN₃. An additional weak shoulder, likely due to the underlying GaNbuffer layer, is observed at 375 nm. The scanning feature of the SEM/CLapparatus was also used to investigate the spatial uniformity andcompositional homogeneity of the films by collecting the CL signal atselected wavelengths while rastering across the sample surface. In theseexperiments three wavelengths were monitored corresponding to themaximum peak value (346 nm), pure GaN (358 nm) and a control valueslightly below the alloy maximum (339 nm). It was found that the spatialintensity distributions at these wavelengths are identical indicating ahigh degree of compositional uniformity in the alloy on a lateral scaleof ˜5 nm.

Example 13 Group III Nitride Growth on Epitaxial LayerAlGaN/GaN/ZrB₂/Si(111)

Similar to the preceding example, an AlGaN overlayer was applied to thestructure of Example 11 to form an AlGaN/GaN/ZrB₂/Si(111)heterostructure. For the present example, the GaN layer adjacent to thesubstrate was formed at 550-600° C. via a single source deposition ofthe H₂GaN₃ compound.

The AlGaN overlayer was formed via reactions of H₂GaN₃ vapors and a beamof Al atoms generated from a solid source in an effusion cell. Thismethod allowed unprecedented low temperature (600° C.) growth conditionsby combining highly energetic single-source CVD with conventionalmolecular beam epitaxy,

Example 14 Theoretical Simulation of the AlGaN/GaN/ZrB₂ Growth

The growth of AlGaN on GaN/ZrB₂ buffered Si via displacement of Ga atomsfrom the adsorbed Ga₃N₃ unit by Al was theoretically studied toelucidate the displacement reaction mechanism leading to the formationof AlGaN. Initially the stability of the (D₂GaN₃)₃ trimeric precursorwas investigated and its subsequent interaction with the ZrB₂ surfacewas modeled using first principles density functional theory (DFT). Thedata indicated that intact Ga₃N₃ units bind strongly via the N atoms onZr terminated surfaces and these units serve as reactive sites forsubsequent displacement of Ga by Al to form AlGaN.

All of our first principles DFT calculations were performed at the GGAlevel using the VASP code. A plane wave cutoff of 350 eV and singlegamma point k-space integration were used in all cases. A computationalcell of dimensions 10.978×12.626×35.3 Å was used to represent the fiveslab of crystalline ZrB₂ with approximately 22 Å of intervening vacuumspace. The initial unreacted configuration was represented by placingthe (D₂GaN₃)₃ molecule above the slab in the center of the vacuumregion. The reacted configurations were initialized by placing thedecomposition byproducts D₂ and N₂ uniformly throughout the same vacuumregion and the (GaN)₃ building blocks in the vicinity of the surface.Free molecule calculations for the trimeric and monomeric molecularstructures were approximated by placing the units within an emptysupercell. Computational errors were minimized by using identicalconditions (cell dimensions, plane wave cutoffs, convergence criteria)for all calculations.

Calculations indicated that the trimeric (D₂GaN₃)₃ is thermodynamicallymore stable than the corresponding D₂GaN₃ monomeric constituents by 4.8eV. This confirms that the adsorption process and subsequent crystalgrowth likely involves the entire (GaN)₃ molecular core of (D₂GaN₃)₃,and not individual Ga—N units derived from monomers.

The initial steps of the growth process were modeled by simulating theadsorption of (D₂GaN₃)₃ on the free Zr and B-terminated surfaces of a 5layer ZrB₂(0001) slab. The (GaN)₃ building block which bonds to the ZrB₂substrate is generated by thermal elimination of the N₂ and D₂ fromgaseous (D₂GaN₃)₃ compound. To simulate this process the net reactionenergy was calculated by comparing the energy of an isolated (D₂GaN₃)₃molecule above the slab, with the energy of the surface bonded (GaN)₃cyclic-core including the D₂ and N₂ byproduct formation.

In this context, the energies associated with the four possibleco-planar (GaN)₃—ZrB₂(0001) bonding orientations were examined. Theseinclude the Ga or N atoms in (GaN)₃ bonded to either the free zirconiumor boron terminated surface of ZrB₂ (0001). The most favorable reactionis found to involve the three N-atoms in (GaN)₃ bonded to theZr-terminated ZrB₂ surface. For this case, calculations yielded a netreaction energy of ˜−4.5 eV per (GaN)₃ unit. This is equivalent to 1.5eV per Zr—N bond, which is compatible with the calculated Zr—N bondenergy of ˜1.6 eV found in the corresponding bulk GaN—ZrB₂ interface.Results showed that the preformed (GaN)₃ building blocks, inherentlypossess the exact Ga—N composition, the precise bonding configurationand the thermodynamic driving force to form a perfectly commensurate andhighly stoichiometric GaN—ZrB₂ interface. Any secondary reactionsleading to the formation of Zr—B—N at the interface are effectivelysuppressed via the incorporation of entire (GaN)₃ units in to the film.

Although specific embodiments have been illustrated and describedherein, it will be appreciated by those of ordinary skill in the artthat any arrangement that is calculated to achieve the same purpose maybe substituted for the specific embodiments shown. This application isintended to cover any adaptations or variations of embodiments of thepresent invention. It is to be understood that the above description isintended to be illustrative, and not restrictive, and that thephraseology or terminology employed herein is for the purpose ofdescription and not of limitation. Combinations of the above embodimentsand other embodiments will be apparent to those of skill in the art uponstudying the above description. The scope of the present inventionincludes any other applications in which embodiment of the abovestructures and fabrication methods are used. The scope of theembodiments of the present invention should be determined with referenceto claims associated with these embodiments, along with the full scopeof equivalents to which such claims are entitled.

1. A semiconductor structure comprising a substrate and an epitaxiallayer formed over the substrate, wherein the epitaxial layer comprises Band one or more element selected from the group consisting of Zr, Hf andAl; and the epitaxial layer has a thickness greater than 50 nm.
 2. Thesemiconductor structure of claim 1, wherein the epitaxial layer has oneor more properties selected from the group consisting of, (i) relaxed at900° C.; (ii) thermally decoupled from the substrate; and (iii) anatomically flat surface.
 3. The semiconductor structure of claim 1wherein the epitaxial layer comprises ZrB₂, AlB₂, or HfB₂.
 4. Thesemiconductor structure of claim 1 wherein the epitaxial layer comprisesan alloy selected from the group consisting of Hf_(x)Zr_(1−x)B₂,Hf_(x)Al_(1−x)B₂, Zr_(x)Al_(1−x)B₂, and Zr_(z)Hf_(y)Al_(1−z−y)B₂,wherein the sum of z and y is less than or equal to
 1. 5. Thesemiconductor structure of claim 1, further comprising an active layerformed over the epitaxial layer.
 6. The semiconductor structure of claim5, wherein the active layer has one or more properties selected from thegroup consisting of (i) lattice-matched to the epitaxial film; (ii)comprising a Group III nitride; and (iii) comprising a compound which isselected from the group consisting of GaN, AlGaN, InGaN, AlInGaN, AlN,InN, and SiCAlN, or mixtures thereof.
 7. The semiconductor structure ofclaim 1, wherein the substrate comprises Si, Al₂O₃, SiC or GaAs.
 8. Thesemiconductor structure of claim 7 wherein the substrate comprisesSi(100) or Si(111).
 9. The semiconductor structure of claim 7 whereinthe substrate comprises a miscut Si(111) substrate.
 10. Thesemiconductor structure of claim 1, wherein the epitaxial layer isformed by molecular beam epitaxy or chemical vapor deposition.
 11. Thesemiconductor structure of claim 1, wherein the epitaxial layer isformed directly on the substrate, and comprises B and two or moreelements selected from the group consisting of Zr, Hf and Al.
 12. Thesemiconductor structure of claim 11, further comprising an epitaxialHfB₂ layer formed directly on the epitaxial layer.
 13. The semiconductorstructure of claim 1, wherein the epitaxial layer is formed directly onthe substrate and comprises ZrB₂.
 14. The semiconductor structure ofclaim 13, further comprising an epitaxial HfB₂ layer formed directly onthe epitaxial layer.
 15. A method for forming an epitaxial buffer layerover a substrate comprising, contacting a substrate with a precursor gasat a temperature and a pressure suitable for depositing an epitaxialbuffer layer over the substrate, the epitaxial buffer layer having athickness of greater than about 50 nm, wherein the precursor gascomprises hydrogen and about 0.1-5 v/v % of a precursor source, whereinthe precursor source comprises Zr(BH₄)₄, Hf(BH₄)₄, an Al source, ormixtures thereof.
 16. The method of claim 15, wherein the substratecomprises Si, Al₂O₃, SiC or GaAs.
 17. The method of claim 16 wherein thesubstrate comprises Si(100) or Si(111).
 18. The method of claim 15wherein the substrate comprises a miscut Si(111) substrate.
 19. Themethod of claim 15 wherein the epitaxial buffer layer comprises ZrB₂,AlB₂, or HfB₂.
 20. The method of claim 15 wherein the epitaxial bufferlayer comprises an alloy selected from the group consisting ofHf_(x)Zr_(1−x)B₂, Hf_(x)Al_(1−x)B₂, Zr_(x)Al_(1−x)B₂, andZr_(z)Hf_(y)Al_(1−z−y)B₂, wherein the sum of z and y is less than orequal to
 1. 21. The method of claim 15 wherein the temperature rangesfrom about 850° C. to about 950° C.
 22. The method of claim 15 whereinthe pressure ranges from about 1×10⁻⁴ Torr to 1×10⁻⁹ Torr.
 23. Themethod of claim 15, wherein the epitaxial layer is formed by molecularbeam epitaxy or chemical vapor deposition.
 24. A method for integratingGroup III nitrides onto a substrate comprising, forming a buffer layerof a diboride of Zr, Hf, Al, or mixtures thereof, having a thicknessgreater than about 50 nm over a substrate; and forming a Group IIInitride layer over the buffer layer.
 25. The method of claim 24, whereinthe buffer layer has one or more properties selected from the groupconsisting of, (i) thermally decoupled from the substrate; (ii) amismatch strain which is essentially thermally constant over atemperature range of room temperature to 900° C.; (iii) relaxed at 900°C.; and (iv) an atomically flat surface.
 26. The method of claim 24,wherein the buffer layer comprises ZrB₂, AlB₂, or HfB₂.
 27. The methodof claim 24 wherein the buffer layer comprises Hf_(x)Zr_(1−x)B₂,Hf_(x)Al_(1−x)B₂, Zr_(x)Al_(1−x)B₂, or Zr_(z)Hf_(y)Al_(1−z−y)B₂, whereinthe sum of z and y is less than or equal to
 1. 28. The method of claim24, wherein the Group III nitride layer has one or more propertiesselected from the group consisting of, (i) lattice-matched to the bufferlayer; and (ii) comprising a compound selected from the group consistingof GaN, AlGaN, InGaN, AlInGaN, AlN, InN, SiCAlN, and mixtures thereof.29. The method of claim 24, wherein the substrate comprises Si, Al₂O₃,SiC or GaAs.
 30. The method of claim 24 wherein the substrate comprisesSi(111) or Si(100).
 31. The method of claim 24 wherein the substratecomprises a miscut Si(111) substrate.
 32. The method of claim 24,wherein the buffer layer is formed by molecular beam epitaxy or chemicalvapor deposition.
 33. A method for tuning the reflectivity of a bufferlayer comprising, forming a buffer layer of an alloy of the formulaHf_(x)Zr_(1−x)B₂ having a thickness greater than about 50 nm and areflectivity over a substrate, wherein x is a predetermined value from 0to 1, and wherein the reflectivity of the buffer layer is greater than alayer of ZrB₂ having an identical thickness as the buffer layer.
 34. Amethod for tuning the lattice constant of a buffer layer comprising,forming a buffer layer of an alloy of the formula Hf_(x)Zr_(1−x)B₂having a thickness greater than about 50 nm, and forming an active layerover the buffer layer, wherein x is a predetermined value from 0 to 1,and wherein the active layer is lattice matched to the buffer layer,